Mathematics: 0/1 Solve the equation by completing the square. Round your answer to the nearest hundredth, if necessary x^2+18x=7

0/1 Solve the equation by completing the square.

muravyevaarina

11.05.2021

The solution to the equation is x = 0.38 or -18.38

Step-by-step explanation:

x^2+18x=7 can be properly written as

$x^{2} +18x =7$

To solve by completing the square, divide the coefficient of x by 2, square and then add to both sides

i.e 18/2 = 9

Then add 9² to both sides of the equation

$x^{2} +18x + 9^{2} = 7 + 9^{2}$

This becomes

$(x+9)^{2} = 7 + 81$

$(x+9)^{2} = 88$

$x+9 = \pm \sqrt{88}$

$x = -9 \pm\sqrt{88}$

$x = -9 \pm 9.38$

∴ x = -9+9.38 or -9-9.38

x = 0.38 or -18.38

Hence, x = 0.38 or -18.38

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