QuestionRewrite the equation $x^{2}-24 x+5$ as $(x+a)^2 + b$ by completing the square, with $a$ and $b$ as integers.

Studdy Solution

STEP 1

Assumptions1. The given quadratic equation is $x^{}-24 x+5$ . . We need to rewrite it in the form $(x+a)^ + b$ where $a$ and $b$ are integers.
3. We will use the method of completing the square to achieve this.

STEP 2

The general form of a quadratic equation is $x^{2} +2bx + c$ . To rewrite the given equation in the form $(x+a)^2 + b$ , we need to make the coefficient of $x$ half of its current value. This can be achieved by dividing the coefficient of $x$ by2.
$a = -\frac{24}{2}$

STEP 3

Calculate the value of $a$ .
$a = -\frac{24}{2} = -12$

STEP 4

Now, we substitute $a$ into the equation $(x+a)^2$ to get $(x-12)^2$ . However, this is not our final equation. We need to subtract the square of $a$ from the constant term in the original equation to find $b$ .
$b = - a^2$

STEP 5

Substitute the value of $a$ into the equation to find $b$ .
$b =5 - (-12)^2$

STEP 6

Calculate the value of $b$ .
$b =5 -144 = -139$

STEP 7

Now, we substitute $a$ and $b$ into the equation $(x+a)^2 + b$ to get our final equation.
$(x-12)^2 -139$ So, the quadratic equation $x^{2}-24 x+5$ can be rewritten as $(x-12)^2 -139$ by completing the square.

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QuestionRewrite the equation $x^{2}-24 x+5$ as $(x+a)^2 + b$ by completing the square, with $a$ and $b$ as integers.

Studdy Solution

STEP 1

Assumptions1. The given quadratic equation is $x^{}-24 x+5$ . . We need to rewrite it in the form $(x+a)^ + b$ where $a$ and $b$ are integers.
3. We will use the method of completing the square to achieve this.

STEP 2

The general form of a quadratic equation is $x^{2} +2bx + c$ . To rewrite the given equation in the form $(x+a)^2 + b$ , we need to make the coefficient of $x$ half of its current value. This can be achieved by dividing the coefficient of $x$ by2.
$a = -\frac{24}{2}$

STEP 3

Calculate the value of $a$ .
$a = -\frac{24}{2} = -12$

STEP 4

Now, we substitute $a$ into the equation $(x+a)^2$ to get $(x-12)^2$ . However, this is not our final equation. We need to subtract the square of $a$ from the constant term in the original equation to find $b$ .
$b = - a^2$

STEP 5

Substitute the value of $a$ into the equation to find $b$ .
$b =5 - (-12)^2$

STEP 6

Calculate the value of $b$ .
$b =5 -144 = -139$

STEP 7

Now, we substitute $a$ and $b$ into the equation $(x+a)^2 + b$ to get our final equation.
$(x-12)^2 -139$ So, the quadratic equation $x^{2}-24 x+5$ can be rewritten as $(x-12)^2 -139$ by completing the square.

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QuestionRewrite the equation x2−24x+5x^{2}-24 x+5x2−24x+5 as (x+a)2+b(x+a)^2 + b(x+a)2+b by completing the square, with aaa and bbb as integers.

Studdy Solution

STEP 1

Assumptions1. The given quadratic equation is x−24x+5x^{}-24 x+5x−24x+5. . We need to rewrite it in the form (x+a)+b(x+a)^ + b(x+a)+b where aaa and bbb are integers.3. We will use the method of completing the square to achieve this.

STEP 2

STEP 3

Calculate the value of aaa.a=−242=−12a = -\frac{24}{2} = -12a=−224​=−12

STEP 4

Now, we substitute aaa into the equation (x+a)2(x+a)^2(x+a)2 to get (x−12)2(x-12)^2(x−12)2. However, this is not our final equation. We need to subtract the square of aaa from the constant term in the original equation to find bbb.b=−a2b = - a^2b=−a2

STEP 5

Substitute the value of aaa into the equation to find bbb.b=5−(−12)2b =5 - (-12)^2b=5−(−12)2

STEP 6

Calculate the value of bbb.b=5−144=−139b =5 -144 = -139b=5−144=−139

STEP 7

Now, we substitute aaa and bbb into the equation (x+a)2+b(x+a)^2 + b(x+a)2+b to get our final equation.(x−12)2−139(x-12)^2 -139(x−12)2−139So, the quadratic equation x2−24x+5x^{2}-24 x+5x2−24x+5 can be rewritten as (x−12)2−139(x-12)^2 -139(x−12)2−139 by completing the square.

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QuestionRewrite the equation $x^{2}-24 x+5$ as $(x+a)^2 + b$ by completing the square, with $a$ and $b$ as integers.

Assumptions1. The given quadratic equation is $x^{}-24 x+5$ . . We need to rewrite it in the form $(x+a)^ + b$ where $a$ and $b$ are integers.
3. We will use the method of completing the square to achieve this.

Calculate the value of $a$ .
$a = -\frac{24}{2} = -12$

Now, we substitute $a$ into the equation $(x+a)^2$ to get $(x-12)^2$ . However, this is not our final equation. We need to subtract the square of $a$ from the constant term in the original equation to find $b$ .
$b = - a^2$

Substitute the value of $a$ into the equation to find $b$ .
$b =5 - (-12)^2$

Calculate the value of $b$ .
$b =5 -144 = -139$

Now, we substitute $a$ and $b$ into the equation $(x+a)^2 + b$ to get our final equation.
$(x-12)^2 -139$ So, the quadratic equation $x^{2}-24 x+5$ can be rewritten as $(x-12)^2 -139$ by completing the square.