Problem Statement
Solve the following quadratic equation and give your answer correct to two decimal places:
$$x^2 - 4x - 8 = 0$$
Verified Solution & Marking Scheme
Apply Quadratic Formula
Here $a = 1, b = -4, c = -8$.
$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \frac{-(-4) \pm \sqrt{(-4)^2 - 4(1)(-8)}}{2(1)} = \frac{4 \pm \sqrt{16 + 32}}{2} = \frac{4 \pm \sqrt{48}}{2}$$
Simplify Radical
$$\sqrt{48} = 4\sqrt{3} \approx 4(1.73205) = 6.9282$$
$$x = \frac{4 \pm 6.9282}{2} = 2 \pm 3.4641$$
Compute Both Roots to Two Decimals
$$x_1 = 2 + 3.4641 = 5.4641 \approx 5.46$$
$$x_2 = 2 - 3.4641 = -1.4641 \approx -1.46$$