Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Sep 16, 2023

Solve for $x$ in $x^2 + 10x + 12 = 36$ . Solutions are $x = -12, 2$ ; $x = -11, 1$ ; $x = -2, 12$ ; $x = -1, 11$ .

STEP 1

Assumptions1. The equation is $x^{}+10 x+12=36$ . We are solving for $x$

STEP 2

First, we need to simplify the equation. We can do this by subtracting36 from both sides of the equation.
$x^{2}+10 x+12-36=0$

STEP 3

implify the equation further.
$x^{2}+10 x-24=0$

STEP 4

Now, we need to factor the quadratic equation. We are looking for two numbers that multiply to -24 and add to10.

STEP 5

The numbers that satisfy these conditions are12 and -2. So, we can write the equation as $(x-2)(x+12)=0$

STEP 6

Now, we can solve for $x$ by setting each factor equal to zero and solving for $x$ .
$x-2=0$ $x+12=0$

STEP 7

olving the first equation gives $x=2$

STEP 8

olving the second equation gives $x=-12$ So, the solutions to the equation $x^{2}+10 x+12=36$ are $x=2$ and $x=-12$ .

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