x^2+15x+15=1
Do you want us to solve for "x"?
x^2+15x+14=0
(x+14)(x+1)=0
x=-14, -1
To solve the equation x^2 + 15x + 15 = 1, we need to rearrange it into the standard quadratic form, which is ax^2 + bx + c = 0.
First, let's subtract 1 from both sides of the equation to isolate the quadratic term:
x^2 + 15x + 15 - 1 = 0
x^2 + 15x + 14 = 0
Now, we can see that a = 1, b = 15, and c = 14.
To solve this quadratic equation, we have a few options:
Option 1: Factoring
We can try to factor the equation if possible. In this case, we need to find two numbers that multiply to 14 and add up to 15. The numbers 2 and 7 satisfy these conditions because 2 * 7 = 14 and 2 + 7 = 9. Therefore, we can rewrite the equation as:
(x + 2)(x + 7) = 0
Now, using the zero product property, we set each factor equal to zero and solve for x:
x + 2 = 0 --> x = -2
x + 7 = 0 --> x = -7
So the solutions to the quadratic equation are x = -2 and x = -7.
Option 2: Quadratic Formula
If factoring is not possible or the factors are hard to find, we can use the quadratic formula to solve the equation. The quadratic formula states that for any quadratic equation ax^2 + bx + c = 0, the solutions for x are given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 1, b = 15, and c = 14. Plugging these values into the quadratic formula, we get:
x = (-15 ± √(15^2 - 4 * 1 * 14)) / (2 * 1)
x = (-15 ± √(225 - 56)) / 2
x = (-15 ± √169) / 2
x = (-15 ± 13) / 2
Simplifying further, we have:
x = (-15 + 13) / 2 --> x = -1
x = (-15 - 13) / 2 --> x = -14
So, the solutions are x = -1 and x = -14.
Both factoring and the quadratic formula can be used to solve the given equation, depending on the complexity of the quadratic expression.