[tex]\boxed{x_{1}=-15} \\ \\ \boxed{x_{2}=-17}[/tex]
Explanation:
In this case, we have the following equation:
[tex]x^2+32x+256=1[/tex]
But we can write this equation as:
[tex]x^2+32x+256=1 \\ \\ Subtract \ -1 \ from\ both \ sides: \\ \\ x^2+32x+256-1=1-1 \\ \\ x^2+32x+255=0[/tex]
So this final result is a quadratic equation written in Standard Form ([tex]ax^2+bx+c=0[/tex]). We need to find the solutions to this equations, so let's use quadratic formula:
[tex]x=\frac{-b \pm \sqrt{b^2-4ac}}{2a} \\ \\ a=1 \\ b=32 \\ c=255 \\ \\ \\ x=\frac{-32 \pm \sqrt{(32)^2-4(1)(255)}}{2(1)} \\ \\ x=\frac{-32 \pm \sqrt{1024-1020}}{2} \\ \\ x=\frac{-32 \pm \sqrt{4}}{2} \\ \\ x=\frac{-32 \pm 2}{2} \\ \\ Finally, \ two \ solutions: \\ \\ \boxed{x_{1}=-15} \\ \\ \boxed{x_{2}=-17}[/tex]
Learn more:
Quadratic Equations: https://brainly.com/question/10278062
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