x 2 +8x+76=−10x−4

The equation you provided is: x^2 + 8x + 76 = -10x - 4.

Let's solve it step by step:

Step 1: Combine like terms on both sides of the equation.

This gives us: x^2 + 8x + 10x + 76 + 4 = 0

Step 2: Simplify the equation.

This gives us: x^2 + 18x + 80 = 0

Step 3: Now, we need to solve for x. This is a quadratic equation, so we can use the quadratic formula, which is x = [-b ± sqrt(b^2 - 4ac)] / (2a). In this equation, a = 1, b = 18, and c = 80.

Step 4: Substitute a, b, and c into the quadratic formula.

This gives us: x = [-18 ± sqrt((18)^2 - 4180)] / (2*1)

Step 5: Simplify the equation.

This gives us: x = [-18 ± sqrt(324 - 320)] / 2

Step 6: Further simplify the equation.

This gives us: x = [-18 ± sqrt(4)] / 2

Step 7: Solve for x.

This gives us: x = [-18 ± 2] / 2

So, the solutions are x = -10 and x = -20.