QuestionJuly 15, 2025

Solve: x^2-8x=24 x=4pm 2sqrt (10) x=-4pm sqrt (40) (1)/(2)+(1)/(2)+(1)/(3)+(1)/(3)+(1)/(3)+(1)/(12)+frac x=2sqrt (10)pm 4

Solve: x^2-8x=24 x=4pm 2sqrt (10) x=-4pm sqrt (40) (1)/(2)+(1)/(2)+(1)/(3)+(1)/(3)+(1)/(3)+(1)/(12)+frac x=2sqrt (10)pm 4
Solve: x^2-8x=24 x=4pm 2sqrt (10) x=-4pm sqrt (40) (1)/(2)+(1)/(2)+(1)/(3)+(1)/(3)+(1)/(3)+(1)/(12)+frac x=2sqrt (10)pm 4

Solution
4.6(252 votes)

Answer

x = 4 \pm 2\sqrt{10} Explanation 1. Rearrange the equation Move 24 to the left side: x^2 - 8x - 24 = 0. 2. Use the quadratic formula **Quadratic formula**: x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}, where a=1, b=-8, c=-24. 3. Calculate the discriminant b^2 - 4ac = (-8)^2 - 4(1)(-24) = 64 + 96 = 160. 4. Solve for x using the quadratic formula x = \frac{8 \pm \sqrt{160}}{2}. 5. Simplify the square root and fraction \sqrt{160} = \sqrt{16 \times 10} = 4\sqrt{10}. x = \frac{8 \pm 4\sqrt{10}}{2} = 4 \pm 2\sqrt{10}.

Explanation

1. Rearrange the equation<br /> Move 24 to the left side: $x^2 - 8x - 24 = 0$.<br /><br />2. Use the quadratic formula<br /> **Quadratic formula**: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, where $a=1$, $b=-8$, $c=-24$.<br /><br />3. Calculate the discriminant<br /> $b^2 - 4ac = (-8)^2 - 4(1)(-24) = 64 + 96 = 160$.<br /><br />4. Solve for x using the quadratic formula<br /> $x = \frac{8 \pm \sqrt{160}}{2}$.<br /><br />5. Simplify the square root and fraction<br /> $\sqrt{160} = \sqrt{16 \times 10} = 4\sqrt{10}$.<br /> $x = \frac{8 \pm 4\sqrt{10}}{2} = 4 \pm 2\sqrt{10}$.
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