Question

solve for x in the equation $x^2 + 10x + 12 = 38$.
$\bigcirc$ $x = -12$ or $x = 2$
$\bigcirc$ $x = -11$ or $x = 1$
$\bigcirc$ $x = -2$ or $x = 12$
$\bigcirc$ $x = -1$ or $x = 11$

Explanation:

Step1: Rearrange the equation

Subtract 38 from both sides to set the equation to zero: \(x^2 + 10x + 12 - 38 = 0\), which simplifies to \(x^2 + 10x - 26 = 0\)? Wait, no, wait. Wait, 12 - 38 is -26? Wait, no, original equation is \(x^2 + 10x + 12 = 38\), so subtract 38: \(x^2 + 10x + 12 - 38 = 0\) → \(x^2 + 10x - 26 = 0\)? Wait, that doesn't seem right. Wait, maybe I made a mistake. Wait, let's check the options. Alternatively, maybe factor by moving all terms to left: \(x^2 + 10x + 12 - 38 = x^2 + 10x - 26 = 0\)? No, that can't be factored. Wait, maybe the original equation was supposed to be \(x^2 + 10x + 12 = 36\)? Wait, the problem says 38. Wait, maybe it's a typo, but let's check the options. Let's test each option.

First option: x = -12 or x = 2. Plug into equation:

For x = -12: \((-12)^2 + 10*(-12) + 12 = 144 - 120 + 12 = 36\). But the right side is 38. Not equal.

For x = 2: \(2^2 + 10*2 + 12 = 4 + 20 + 12 = 36\). Not 38. So first option is wrong.

Second option: x = -11 or x = 1.

x = -11: \((-11)^2 + 10*(-11) + 12 = 121 - 110 + 12 = 23\). Not 38.

x = 1: \(1 + 10 + 12 = 23\). Not 38. Wrong.

Third option: x = -2 or x = 12.

x = -2: \((-2)^2 + 10*(-2) + 12 = 4 - 20 + 12 = -4\). Not 38.

x = 12: \(144 + 120 + 12 = 276\). Not 38. Wrong.

Fourth option: x = -1 or x = 11.

x = -1: \((-1)^2 + 10*(-1) + 12 = 1 - 10 + 12 = 3\). Not 38. Wait, this is not working. Wait, maybe the original equation was \(x^2 + 10x + 12 = 36\). Let's check. If it's 36, then:

x^2 +10x +12 -36 = x^2 +10x -24 = 0. Factor: (x+12)(x-2)=0 → x=-12 or x=2. Which is the first option. But the problem says 38. Maybe a typo. Alternatively, maybe I miscalculated. Wait, let's re-express the original equation:

x² +10x +12 = 38 → x² +10x = 26 → x² +10x +25 = 26 +25 → (x+5)² = 51 → x+5 = ±√51 → x = -5 ±√51 ≈ -5 ±7.14 → x≈2.14 or x≈-12.14. Which is close to x=-12 or x=2. So maybe the problem meant 36 instead of 38. So the first option is the intended answer.

Step2: Verify the options

Assuming the equation is x² +10x +12 = 36 (a common problem), then solving:

x² +10x +12 -36 = x² +10x -24 = 0.

Factor: (x + 12)(x - 2) = 0.

Thus, x = -12 or x = 2. Which matches the first option.

Answer:

A. \( x = -12 \) or \( x = 2 \)