What are the exact solutions?
x^2+4x+4=36
I have -34,-38
Is this right?
I am not exactly sure if this answer is correct. I ran it through my Calculator and here is what I get..
X2+4x+4=36
= x2+4x-32=0
=x2-4x+8x-32=0
=x(x2/x – 22*x/x) + 23 (23*x/23- 25/23) = 0
= x(x-4) +23 (x-4) = 0
= (x-4) (x+8) = 0
= x - 4 = 0
= x +4 = 0
X = 4
X = -8
X = 4, -8
Becky, why did you not substitute your answers back in the equation.
It would have shown you that you are way off,
but Mike's answers work and his solution is correct.
To find the exact solutions of the equation x^2 + 4x + 4 = 36, we need to solve the equation for x. Let's go step by step.
First, we need to move the constant term (-36) to the other side of the equation:
x^2 + 4x + 4 - 36 = 0
Simplifying this equation, we get:
x^2 + 4x - 32 = 0
Now, we can try to factor the quadratic equation. However, this equation does not easily factor, so we have to use another method to solve it.
One common method to solve quadratic equations is by using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Comparing our equation to the standard quadratic equation form (ax^2 + bx + c = 0), we can see that a = 1, b = 4, and c = -32.
Plugging in these values into the quadratic formula, we have:
x = (-(4) ± √((4)^2 - 4(1)(-32))) / (2(1))
Simplifying further:
x = (-4 ± √(16 + 128)) / 2
x = (-4 ± √144) / 2
x = (-4 ± 12) / 2
This gives us two possible solutions:
x = (-4 + 12) / 2 = 8 / 2 = 4
x = (-4 - 12) / 2 = -16 / 2 = -8
Therefore, the exact solutions to the equation x^2 + 4x + 4 = 36 are x = 4 and x = -8.
So, the solutions you provided, -34 and -38, are not correct. The correct solutions are x = 4 and x = -8.