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Quadratic formula decimal answer solve the equation to the nearest tenth

Quadratic formula decimal answer solve the equation to the nearest tenth-example-1

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First, recall that given the equation


ax^2+b+c=0

The solutions are given by


x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}

where the sign in the middle means that we get one root by taking a plus sign and we get the other root by taking a minus sign.

In our case, we have a=1, b=-6 and c=-41. So the solutions of this equation are given by


x=\frac{-(-6)\pm\sqrt[]{(-6)^2-4(-41)}}{2}=\frac{6\pm\sqrt[]{36+164}}{2}=\frac{6\pm\sqrt[]{200}}{2}

Note that


\sqrt[]{200}=\sqrt[]{100\cdot2}=\sqrt[]{100}\cdot\sqrt[]{2}=10\sqrt[]{2}

Then


x=\frac{6\pm10\sqrt[]{2}}{2}=3\pm5\sqrt[]{2}

taking sqrt(2) as 1.4142, we get


x=3+5\cdot\sqrt[]{2}=10.071\approx10

and


x=3-5\sqrt[]{2}=-4.071\approx-4

User Mostafa Mohsen
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