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Mathematics

Use quadratic formula to solve:

x2 = 4x

Quadratic Equations

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Answer

Given,

x2 = 4x

x2 - 4x = 0

Comparing x2 - 4x = 0 with ax2 + bx + c = 0 we get,

a = 1, b = -4 and c = 0.

We know that,

x = −b±b2−4ac2a\dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Substituting values of a, b and c in above equation we get,

⇒x=−(−4)±(−4)2−4(1)(0)2(1)=4±16−02=4±42=4+42 or 4−42=82 or 02=4 or 0.\Rightarrow x = \dfrac{-(-4) \pm \sqrt{(-4)^2 - 4(1)(0)}}{2(1)} \\[1em] = \dfrac{4 \pm \sqrt{16 - 0}}{2} \\[1em] = \dfrac{4 \pm 4}{2} \\[1em] = \dfrac{4 + 4}{2} \text{ or } \dfrac{4 - 4}{2} \\[1em] = \dfrac{8}{2} \text{ or } \dfrac{0}{2} \\[1em] = 4 \text{ or } 0.

Hence, x = 0 or 4.

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