Final answer:
To complete the square for the quadratic equation 9x^2 + 12x + 5 = 10, rearrange the equation, add a constant to both sides to make it a perfect square, and solve for x, which comes to -2 after calculation.
Step-by-step explanation:
To complete the square for the quadratic equation 9x^2 + 12x + 5 = 10, we need to rearrange the equation to have the x terms on one side and the constant terms on the other side.
First, subtract 10 from both sides: 9x^2 + 12x - 5 = 0.
Now, take half of the coefficient of x (which is 12) and square it.
Half of 12 is 6, and 6 squared is 36.
Add 36 to both sides:
9x^2 + 12x + 36 - 5 - 36 = 0.
Simplify:
9x^2 + 12x + 31 = 0.
The left side of the equation can now be factored into a perfect square:
(3x + 6)^2 = 0.
Take the square root of both sides: 3x + 6 = 0.
Then, solve for x: x = -2.