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Solve the equation 2x^2 - 10x + 35 = x^2 + 10.

 Jun 23, 2020
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Move the terms around so we have a quadratic equation.

 

\(2x^2-10x+35=x^2+10\\ x^2-10x-25=0\)

 

Now we can simply solve for x using the quadratic formula. Let a=1, b=-10, and c=-25.

 

\(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\ x=\frac{10\pm\sqrt{(-10)^2-4(1)(-25)}}{2(1)}\\ x=\frac{10\pm\sqrt{200}}{2}\\ x=\frac{10\pm10\sqrt{2}}{2}\\ x=5\pm5\sqrt{2} \)

 

So x is \(5+\sqrt{2}\ \text{and}\ 5-\sqrt{2}\).

 Jun 23, 2020

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