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Solve x^2 + 2x - 8 = 0

Worked through step by step. More quadratics.

Answer
x=−4, x=2\boxed{x = -4, \, x = 2}

Checking the result, (−4)2+2(−4)−8=16−8−8=0(-4)^2 + 2(-4) - 8 = 16 - 8 - 8 = 0 and (2)2+2(2)−8=4+4−8=0(2)^2 + 2(2) - 8 = 4 + 4 - 8 = 0, so both solutions are correct.

Problem: Solve the quadratic equation x2+2x−8=0x^2 + 2x - 8 = 0.

Steps

  1. Factor the quadratic expression
    (x+4)(x−2)=0(x + 4)(x - 2) = 0
  2. Apply the zero product property
    x+4=0orx−2=0x + 4 = 0 \quad \text{or} \quad x - 2 = 0
  3. Solve for xx in the first equation
    x=−4x = -4
  4. Solve for xx in the second equation
    x=2x = 2

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