7x² = 9 + x Subtract x from both sides
7x² - x = 9 Subtract 9 from both sides
7x² - x - 9 = 0 Use the Quadratic Formula
a = 7 , b = -1 , c = -9
x = [tex] \frac{-b \pm \sqrt{b^2 - 4ac} }{2a} [/tex] Plug in the a, b, and c values
x = [tex] \frac{- (-1) \pm \sqrt{(-1)^2 - 4(7)(-9)} }{2(7)} [/tex] Cancel out the double negative
x = [tex] \frac{1 \pm \sqrt{(-1)^2 - 4(7)(-9)} }{2(7)} [/tex] Square -1
x = [tex] \frac{1 \pm \sqrt{1 - 4(7)(-9)} }{2(7)} [/tex] Multiply 7 and -9
x = [tex] \frac{1 \pm \sqrt{1 - 4(-63} }{2(7)} [/tex] Multiply -4 and -63
x = [tex] \frac{1 \pm \sqrt{1 + 252} }{2(7)} [/tex] Multiply 2 and 7
x = [tex] \frac{1 \pm \sqrt{1 + 252} }{14} [/tex] Add 1 and 252
x = [tex] \frac{1 \pm \sqrt{253} }{14} [/tex] Split up the [tex]\pm[/tex]
x = [tex] \left \{ {{ \frac{1 + \sqrt{253} }{14} } \atop { \frac{1 - \sqrt{253} }{14} }} \right. [/tex]
The approximate square root of 253 is 15.905973.
x ≈ [tex] \left \{ { \frac{1 + 15.905973}{14} } \atop { \frac{1 - 15.905973}{14} }} \right [/tex] Add and subtract
x ≈ [tex] \left \{ {{ \frac{16.905973}{14} } \atop { \frac{14.905973}{14} }} \right. [/tex] Divide
x ≈ [tex] \left \{ {{1.2075} \atop {1.0647}} \right. [/tex] Round to the nearest hundredth
x ≈ [tex] \left \{ {{1.21} \atop {1.06}} \right. [/tex]
