Solve -x^2+2x+8

Solve ax² + bx + c = 0 using the quadratic formula with discriminant analysis.

Equation

Answer

x = -2, 4

-x²+2x+8

Solve by factoring the quadratic and applying the zero product property:

Multiply by −1:

x² − 2x − 8 = 0

Step 1 — Factor the quadratic

We need two numbers that multiply to -8 (the constant term) and add to -2 (the coefficient of x):

-4 × 2 = -8 and -4 + 2 = -2

Write the factored form using these numbers:

(x - 4)(x + 2) = 0

Step 2 — Apply the zero product property

If a product equals zero, at least one of the factors must be zero. Set each factor equal to zero and solve:

x − 4 = 0 → x = 4

x + 2 = 0 → x = −2

x = -2, 4

How to solve -x^2+2x+8

To solve -x^2+2x+8, we can try factoring, use the quadratic formula, or complete the square. The solution is x = -2, 4.

This is a second-degree quadratic equation — the highest power of the variable is 2. Quadratic equations can have two real roots, one repeated root, or two complex roots.

Frequently asked questions

What is the answer to -x^2+2x+8?
The answer is x = -2, 4.

What method is used?
factoring when possible, or the quadratic formula x = (−b ± √(b²−4ac)) / 2a. The discriminant b²−4ac determines the number and type of solutions.

How do I verify this?
Substituting the solution(s) back into -x^2+2x+8 confirms both sides are equal.

More quadratic formula calculator problems

x² + 5x + 6 = 0 x² − 4 = 0 2x² − 3x − 2 = 0 x² + 2x − 8 = 0 x² − 6x + 9 = 0 3x² + x − 2 = 0 x² − 9 = 0 x² + 4x + 4 = 0 x² − x − 12 = 0 4x² − 1 = 0 x² + 3x = 10 2x² = 18