This is the fantastic "QUADRATIC" math problem

Algebra Level 2

Solve 5 x 2 − 3 x + 2 = 4 5x^2-3x+2=4

6 or 8 1 or -0.4 5 or 3.4 2 or 3

Harsh Chaudhari by Harsh Chaudhari , 36, India

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2 solutions

Chew-Seong Cheong
Oct 17, 2019

5 x 2 − 3 x + 2 = 4 5 x 2 − 3 x − 2 = 0 ( 5 x + 2 ) ( x − 1 ) = 0 ⟹ x = − 0.4 , 1 \begin{aligned} 5x^2 - 3x+2 & = 4 \\ 5x^2 - 3x - 2 & = 0 \\ (5x + 2)(x-1) & = 0 \\ \implies x & = \boxed {-0.4, 1} \end{aligned}

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5 x 2 − 3 x + 2 = 4 5x^2-3x+2=4

5 x 2 − 3 x − 2 = 0 5x^2-3x-2=0

By the quadratic formula,

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

x = 3 ± ( − 3 ) 2 − 4 ( 5 ) ( − 2 ) 2 ( 5 ) x=\dfrac{3 \pm \sqrt{(-3)^2-4(5)(-2)}}{2(5)}

x = 3 ± 9 + 40 10 x=\dfrac{3 \pm \sqrt{9+40}}{10}

x = 3 ± 49 10 x=\dfrac{3 \pm \sqrt{49}}{10}

x = 3 ± 7 10 x=\dfrac{3 \pm 7}{10}

x = 3 + 7 10 = 10 10 = 1 x=\dfrac{3 + 7}{10}=\dfrac{10}{10}=1

or

x = 3 − 7 10 = − 4 10 = − 0.4 x=\dfrac{3 - 7}{10}=\dfrac{-4}{10}=-0.4

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