QuestionSolve the equation $x^{2}-24 x+143=0$ .

Studdy Solution

STEP 1

Assumptions1. The given equation is a quadratic equation of the form $ax^ + bx + c =0$ . We are asked to solve for $x$

STEP 2

The quadratic formula is used to solve equations of the form $ax^2 + bx + c =0$ . The formula is given by $x = \frac{-b \pm \sqrt{b^2 -4ac}}{2a}$

STEP 3

Identify the coefficients $a$ , $b$ , and $c$ from the given equation $x^{2}-24x+143=0$ . Here, $a=1$ , $b=-24$ , and $c=143$ .

STEP 4

Substitute the values of $a$ , $b$ , and $c$ into the quadratic formula.
$x = \frac{-(-24) \pm \sqrt{(-24)^2 -41143}}{2*1}$

STEP 5

implify the equation.
$x = \frac{24 \pm \sqrt{576 -572}}{2}$

STEP 6

Further simplify the equation.
$x = \frac{24 \pm \sqrt{4}}{2}$

STEP 7

Take the square root of4.
$x = \frac{24 \pm2}{2}$

STEP 8

olve for $x$ by using the plus and minus signs separately.
$x = \frac{24 +2}{2} \quad or \quad x = \frac{24 -2}{2}$

STEP 9

implify to find the two solutions for $x$ .
$x =13 \quad or \quad x =11$ The solutions to the equation $x^{2}-24x+143=$ are $x =13$ and $x =11$ .

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

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

Parents Influencer program Contact Policy Terms