Answer:
x = [tex]\frac{7-3\sqrt{13}}{2}[/tex] x= [tex]\frac{7-3\sqrt{13}}{2}[/tex]
Step-by-step explanation:
Step 1: Subtract 7x on both sides
[tex]x^{2} = 7x + 17[/tex]
Step 2: Subtract 17 on both sides
[tex]x^{2} - 7x = 17\\x^{2} -7x - 17 = 0[/tex]
Solve with the quadratic formula:
[tex]\quad x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]\mathrm{For\:}\quad a=1,\:b=-7,\:c=-17:\quad x_{1,\:2}=\frac{-\left(-7\right)\pm \sqrt{\left(-7\right)^2-4\cdot \:1\left(-17\right)}}{2\cdot \:1}[/tex]
[tex]\frac{-\left(-7\right)+\sqrt{\left(-7\right)^2-4\cdot \:1\cdot \left(-17\right)}}{2\cdot \:1}[/tex]
= [tex]\frac{7+\sqrt{117}}{2\cdot \:1}[/tex]
= [tex]\frac{7+\sqrt{117}}{2}[/tex]
= [tex]\frac{7+3\sqrt{13}}{2}[/tex]
[tex]\frac{-\left(-7\right)-\sqrt{\left(-7\right)^2-4\cdot \:1\cdot \left(-17\right)}}{2\cdot \:1}[/tex]
= [tex]\frac{7-\sqrt{117}}{2\cdot \:1}[/tex]
= [tex]\frac{7-\sqrt{117}}{2}[/tex]
= [tex]\frac{7-3\sqrt{13}}{2}[/tex]
x = [tex]\frac{7-3\sqrt{13}}{2}[/tex] x= [tex]\frac{7-3\sqrt{13}}{2}[/tex]
