Solve x^2+3x = 10

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

Equation

Answer

x = -5, 2

x²+3x=10

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

Subtract 10 from both sides:

x² + 3x − 10 = 0

Step 1 — Factor the quadratic

We need two numbers that multiply to -10 (the constant term) and add to 3 (the coefficient of x):

5 × -2 = -10 and 5 + (-2) = 3

Write the factored form using these numbers:

(x - 2)(x + 5) = 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 − 2 = 0 → x = 2

x + 5 = 0 → x = −5

x = -5, 2

How to solve x^2+3x = 10

To solve x^2+3x = 10, we can try factoring, use the quadratic formula, or complete the square. The solution is x = -5, 2.

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+3x = 10?
The answer is x = -5, 2.

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+3x = 10 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