Question

-3x^2-9x+357=9x solve by completing the square

Answer 1

`x_1 = -3 + 8√(2) = 8.3137\\\\x_1 = -3 - 8√(2) = -14.3137\\`

Explanation:

`-3x^2-9x+357=9x\\\\\mathrm{Move}\:357\:\mathrm{to\:the\:right\:side}\\\\-3x^2-18x=-357\\\\\mathrm{Divide\:both\:sides\:by\:}-3\\\\(-3x^2-18x)/(-3)=(-357)/(-3)\\\\x^2+6x=119`

`\mathrm{Rewrite\:in\:the\:form}\:\left(x+a\right)^2=b`

`\left(x+a\right)^2=x^2+2ax+a^2`

`\mathrm{Rewrite\:in\:the\:form}\:x^2+2ax+a^2\\\\\mathrm{Comparing terms }2ax=6x\\\\a=3\\\\\mathrm{Add\:}a^2=3^2\mathrm{\:to\:both\:sides}\\\\x^2+6x+3^2=119+3^2\\\\\left(x+3\right)^2=128\\\\`

`\mathrm{Taking square roots on either side:}\\\\(x + 3) = \pm √(128)\\\\x = -3 \pm √(128)`

`128 = 64 \cdot 2\\\\√(128) = √(64) \cdot √(2)\\\\= 8√(2)`

So the two roots are

`x_1 = -3 + 8√(2) = 8.3137\\\\x_1 = -3 - 8√(2) = -14.3137\\`