1Cademy - Solving $$x^2 + 2x - 8 = 0$$ by Factoring

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Quadratic Equation

Example

Solving $x^2 + 2x - 8 = 0$ by Factoring

Solve $x^2 + 2x - 8 = 0$ by applying the five-step factoring method for quadratic equations.

Step 1 — Write in standard form. The equation $x^2 + 2x - 8 = 0$ is already in the form $ax^2 + bx + c = 0$ , so no rearranging is needed.

Step 2 — Factor the quadratic expression. Find two numbers whose product is $-8$ and whose sum is $2$ . The pair $4$ and $-2$ works: $4 \cdot (-2) = -8$ and $4 + (-2) = 2$ . Therefore:

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

Step 3 — Apply the Zero Product Property. Set each factor equal to zero:

$x + 4 = 0 \quad \text{or} \quad x - 2 = 0$

Step 4 — Solve each linear equation:

$x = -4 \quad \text{or} \quad x = 2$

Step 5 — Check both solutions by substituting into the original equation:

For $x = -4$ : $(-4)^2 + 2(-4) - 8 = 16 - 8 - 8 = 0$ ✓

For $x = 2$ : $(2)^2 + 2(2) - 8 = 4 + 4 - 8 = 0$ ✓

The solutions are $x = -4$ and $x = 2$ . This example demonstrates the simplest case of the factoring method: the equation is already in standard form, so the process begins directly with factoring the trinomial on the left side.

Updated 2026-04-21

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