Final answer:
The equation x^2 +8x -12=0 is already in the standard form of a quadratic equation. To solve it, apply the quadratic formula with 'a' being 1, 'b' being 8, and 'c' being -12 to find the roots of the equation and we get x = (-8 ± √(112)) / 2.
Step-by-step explanation:
Solving Quadratic Equations in Standard Form
The equation x^2 +8x -12=0 is already in the standard form of a quadratic equation, which is ax^2 + bx + c = 0. To solve this equation, you can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a), where 'a' is the coefficient of x^2, 'b' is the coefficient of x, and 'c' is the constant term.
In this case, 'a' is 1, 'b' is 8, and 'c' is -12. Substituting these values into the quadratic formula gives the solutions for x:
x = (-8 ± √(8^2 - 4×1×(-12))) / (2×1),
which simplifies to:
x = (-8 ± √(64 + 48)) / 2,
and further x = (-8 ± √(112)) / 2,
resulting in two possible values for x, which are the roots of the equation.