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Mathematics

Solve the following equation using the formula :

x2 + 6x - 10 = 0

Quadratic Equations

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Answer

Comparing x2 + 6x - 10 = 0 with ax2 + bx + c = 0 we get,

a = 1, b = 6, c = -10.

We know that,

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

Substituting values we get,

⇒x=−(6)±(6)2−4(1)(−10)2(1)=−6±36+402=−6±762=−6±2192=−3±19=−3+4.36 or −3−4.36=1.36 or −7.36\Rightarrow x = \dfrac{-(6) \pm \sqrt{(6)^2 - 4(1)(-10)}}{2(1)} \\[1em] = \dfrac{-6 \pm \sqrt{36 + 40}}{2} \\[1em] = \dfrac{-6 \pm \sqrt{76}}{2} \\[1em] = \dfrac{-6 \pm 2\sqrt{19}}{2} \\[1em] = -3 \pm \sqrt{19} \\[1em] = -3 + 4.36 \text{ or } -3 - 4.36 \\[1em] = 1.36 \text{ or } -7.36

Hence, x = 1.36, -7.36.

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