106th Problem 2016

Algebra Level 2

Solve the quadratic equation:

2 x 2 − 10 x + 35 = x 2 + 10 { 2x }^{ 2 }-10x+35= {x }^{ 2 }+10

Check out the set: 2016 Problems .
x = 5 only x=5 \text{ only} x = ± 5 x=\pm 5 x = − 1 5 only x=- \dfrac { 1 }{ 5} \text{ only} x = − 5 only x=-5 \text{ only}

Angela Fajardo by Angela Fajardo , 19, Philippines

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2 solutions

. .
May 21, 2021

2 x 2 − 10 x + 35 = x 2 + 10 x 2 − 10 x + 25 = 0 ( x − 5 ) 2 ∴ x = 5 \begin{aligned} 2x ^ { 2 } - 10x + 35 = x ^ { 2 } + 10 \\ x ^ { 2 } - 10x + 25 = 0 \\ ( x - 5 ) ^ { 2 } \\ \therefore x = 5 \end{aligned} .

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Ashish Menon
Apr 24, 2016

2 x 2 − 10 x + 35 = x 2 + 10 x 2 − 10 x + 25 = 0 ( x − 5 ) 2 = 0 x − 5 = 0 x = 5 \begin{aligned} 2x^2 - 10x + 35 = x^2 + 10\\ x^2 - 10x + 25 = 0\\ {(x - 5)}^2 = 0\\ x - 5 = 0\\ x = \boxed{5} \end{aligned}

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