Answer:
12.3246
Step-by-step explanation:
The equation to be solved is [tex]x^{2} -10=4x[/tex]
Rearranging: [tex]x^{2} -4x-12=0[/tex]
The quadratic formula is one way to solve this equation.
[tex]x=\frac{-b+\sqrt{b^{2} -4ac} }{2a}=\frac{12+\sqrt{12^{2}-4*1*4} }{2*1}[/tex]
Note that only the positive variation of the quadratic formula was used. This is because it is the only variation of this formula that produces a positive result for this equation. This is not always true, so it is best to work both versions of the formula for problems like these.
[tex]x=\frac{12+\sqrt{160} }{2} =\frac{12+4\sqrt{10} }{2}=6+2\sqrt{10} =6+6.3246=12.3246[/tex]
If the negative version of the quadratic equation was used, the final (incorrect) answer would be x= -0.3246.
