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