QuestionSolve the equation $-x^{2}-9=6 x$ for the variable $x$ .

Studdy Solution

STEP 1

Assumptions1. The equation is $-x^{}-9=6 x$ . We need to solve for $x$

STEP 2

First, we need to rearrange the equation to a standard quadratic form $ax^2 + bx + c =0$ . We can do this by adding $x^2$ and subtracting $6x$ from both sides of the equation.
$-x^{2} -6x -9 =0$

STEP 3

Now, we have the equation in the standard quadratic form. $x^{2} +6x -9 =0$

STEP 4

Next, we can solve the quadratic equation using the quadratic formula $x = \frac{-b \pm \sqrt{b^2 -4ac}}{2a}$ .

STEP 5

First, identify the values of $a$ , $b$ , and $c$ in the equation $x^{2} +x -9 =0$ .
$a =1, b =, c = -9$

STEP 6

Now, plug in the values of $a$ , $b$ , and $c$ into the quadratic formula.
$x = \frac{-6 \pm \sqrt{6^2 -41(-9)}}{2*1}$

STEP 7

implify the equation inside the square root.
$x = \frac{-6 \pm \sqrt{36 +36}}{2}$

STEP 8

Calculate the value inside the square root.
$x = \frac{-6 \pm \sqrt{72}}{2}$

STEP 9

implify the square root.
$x = \frac{-6 \pm6\sqrt{2}}{2}$

STEP 10

Finally, divide all terms by2 to get the solutions for $x$ .
$x = -3 \pm3\sqrt{2}$ The solutions for the equation $-x^{2}-9=6 x$ are $x = -3 +3\sqrt{2}$ and $x = -3 -3\sqrt{2}$ .

Was this helpful?

QuestionSolve the equation $-x^{2}-9=6 x$ for the variable $x$ .

Studdy Solution

STEP 1

Assumptions1. The equation is $-x^{}-9=6 x$ . We need to solve for $x$

STEP 2

First, we need to rearrange the equation to a standard quadratic form $ax^2 + bx + c =0$ . We can do this by adding $x^2$ and subtracting $6x$ from both sides of the equation.
$-x^{2} -6x -9 =0$

STEP 3

Now, we have the equation in the standard quadratic form. $x^{2} +6x -9 =0$

STEP 4

Next, we can solve the quadratic equation using the quadratic formula $x = \frac{-b \pm \sqrt{b^2 -4ac}}{2a}$ .

STEP 5

First, identify the values of $a$ , $b$ , and $c$ in the equation $x^{2} +x -9 =0$ .
$a =1, b =, c = -9$

STEP 6

Now, plug in the values of $a$ , $b$ , and $c$ into the quadratic formula.
$x = \frac{-6 \pm \sqrt{6^2 -41(-9)}}{2*1}$

STEP 7

implify the equation inside the square root.
$x = \frac{-6 \pm \sqrt{36 +36}}{2}$

STEP 8

Calculate the value inside the square root.
$x = \frac{-6 \pm \sqrt{72}}{2}$

STEP 9

implify the square root.
$x = \frac{-6 \pm6\sqrt{2}}{2}$

STEP 10

Finally, divide all terms by2 to get the solutions for $x$ .
$x = -3 \pm3\sqrt{2}$ The solutions for the equation $-x^{2}-9=6 x$ are $x = -3 +3\sqrt{2}$ and $x = -3 -3\sqrt{2}$ .

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionSolve the equation −x2−9=6x-x^{2}-9=6 x−x2−9=6x for the variable xxx.

Studdy Solution

STEP 1

Assumptions1. The equation is −x−9=6x-x^{}-9=6 x−x−9=6x . We need to solve for xxx

STEP 2

First, we need to rearrange the equation to a standard quadratic form ax2+bx+c=0ax^2 + bx + c =0ax2+bx+c=0. We can do this by adding x2x^2x2 and subtracting 6x6x6x from both sides of the equation.−x2−6x−9=0-x^{2} -6x -9 =0−x2−6x−9=0

STEP 3

Now, we have the equation in the standard quadratic form.x2+6x−9=0x^{2} +6x -9 =0x2+6x−9=0

STEP 4

Next, we can solve the quadratic equation using the quadratic formula x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 -4ac}}{2a}x=2a−b±b2−4ac​​.

STEP 5

First, identify the values of aaa, bbb, and ccc in the equation x2+x−9=0x^{2} +x -9 =0x2+x−9=0.a=1,b=,c=−9a =1, b =, c = -9a=1,b=,c=−9

STEP 6

Now, plug in the values of aaa, bbb, and ccc into the quadratic formula.x=−6±62−4∗1∗(−9)2∗1x = \frac{-6 \pm \sqrt{6^2 -4*1*(-9)}}{2*1}x=2∗1−6±62−4∗1∗(−9)​​

STEP 7

implify the equation inside the square root.x=−6±36+362x = \frac{-6 \pm \sqrt{36 +36}}{2}x=2−6±36+36​​

STEP 8

Calculate the value inside the square root.x=−6±722x = \frac{-6 \pm \sqrt{72}}{2}x=2−6±72​​

STEP 9

implify the square root.x=−6±622x = \frac{-6 \pm6\sqrt{2}}{2}x=2−6±62​​

STEP 10

Finally, divide all terms by2 to get the solutions for xxx.x=−3±32x = -3 \pm3\sqrt{2}x=−3±32​The solutions for the equation −x2−9=6x-x^{2}-9=6 x−x2−9=6x are x=−3+32x = -3 +3\sqrt{2}x=−3+32​ and x=−3−32x = -3 -3\sqrt{2}x=−3−32​.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionSolve the equation $-x^{2}-9=6 x$ for the variable $x$ .

Assumptions1. The equation is $-x^{}-9=6 x$ . We need to solve for $x$

First, we need to rearrange the equation to a standard quadratic form $ax^2 + bx + c =0$ . We can do this by adding $x^2$ and subtracting $6x$ from both sides of the equation.
$-x^{2} -6x -9 =0$

Now, we have the equation in the standard quadratic form. $x^{2} +6x -9 =0$

Next, we can solve the quadratic equation using the quadratic formula $x = \frac{-b \pm \sqrt{b^2 -4ac}}{2a}$ .

First, identify the values of $a$ , $b$ , and $c$ in the equation $x^{2} +x -9 =0$ .
$a =1, b =, c = -9$

Now, plug in the values of $a$ , $b$ , and $c$ into the quadratic formula.
$x = \frac{-6 \pm \sqrt{6^2 -41(-9)}}{2*1}$

implify the equation inside the square root.
$x = \frac{-6 \pm \sqrt{36 +36}}{2}$

Calculate the value inside the square root.
$x = \frac{-6 \pm \sqrt{72}}{2}$

implify the square root.
$x = \frac{-6 \pm6\sqrt{2}}{2}$

Finally, divide all terms by2 to get the solutions for $x$ .
$x = -3 \pm3\sqrt{2}$ The solutions for the equation $-x^{2}-9=6 x$ are $x = -3 +3\sqrt{2}$ and $x = -3 -3\sqrt{2}$ .