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-8x(x-1)-x-11=-9(x+4)+17
We move all terms to the left:
-8x(x-1)-x-11-(-9(x+4)+17)=0
We add all the numbers together, and all the variables
-1x-8x(x-1)-(-9(x+4)+17)-11=0
We multiply parentheses
-8x^2-1x+8x-(-9(x+4)+17)-11=0
We calculate terms in parentheses: -(-9(x+4)+17), so:We add all the numbers together, and all the variables
-9(x+4)+17
We multiply parentheses
-9x-36+17
We add all the numbers together, and all the variables
-9x-19
Back to the equation:
-(-9x-19)
-8x^2+7x-(-9x-19)-11=0
We get rid of parentheses
-8x^2+7x+9x+19-11=0
We add all the numbers together, and all the variables
-8x^2+16x+8=0
a = -8; b = 16; c = +8;
Δ = b2-4ac
Δ = 162-4·(-8)·8
Δ = 512
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{512}=\sqrt{256*2}=\sqrt{256}*\sqrt{2}=16\sqrt{2}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16\sqrt{2}}{2*-8}=\frac{-16-16\sqrt{2}}{-16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16\sqrt{2}}{2*-8}=\frac{-16+16\sqrt{2}}{-16} $
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