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Algebra · Quadratic-Equations

Solve x^2 = 2

x^{2} = 2

Step by step

  1. x^{2} = 2

    Start from the equation as given.

  2. x^{2} - 2 = 0

    Bring everything to one side and collect like terms so the right-hand side is 0.

  3. a = 1,\quad b = 0,\quad c = -2

    Read off the coefficients of the standard form ax² + bx + c = 0.

  4. \Delta = b^2 - 4ac = (0)^2 - 4(1)(-2) = 8

    It does not factor nicely, so use the discriminant Δ = b² − 4ac.

  5. x = \frac{-b \pm \sqrt{\Delta}}{2a} = \frac{0 \pm \sqrt{8}}{2}

    Δ > 0, so there are two distinct real roots. Substitute into the quadratic formula.

  6. x = \sqrt{2} \approx 1.4142 \quad\text{or}\quad x = - \sqrt{2} \approx -1.4142

    Simplify each root.

Reveal the answer
x = \sqrt{2} \quad\text{or}\quad x = - \sqrt{2}