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(x+7)(x+7)=252
We move all terms to the left:
(x+7)(x+7)-(252)=0
We multiply parentheses ..
(+x^2+7x+7x+49)-252=0
We get rid of parentheses
x^2+7x+7x+49-252=0
We add all the numbers together, and all the variables
x^2+14x-203=0
a = 1; b = 14; c = -203;
Δ = b2-4ac
Δ = 142-4·1·(-203)
Δ = 1008
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1008}=\sqrt{144*7}=\sqrt{144}*\sqrt{7}=12\sqrt{7}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-12\sqrt{7}}{2*1}=\frac{-14-12\sqrt{7}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+12\sqrt{7}}{2*1}=\frac{-14+12\sqrt{7}}{2} $
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