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4x^{2}-39-10=0
Subtract 10 from both sides.
4x^{2}-49=0
Subtract 10 from -39 to get -49.
\left(2x-7\right)\left(2x+7\right)=0
Consider 4x^{2}-49. Rewrite 4x^{2}-49 as \left(2x\right)^{2}-7^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).
x=\frac{7}{2} x=-\frac{7}{2}
To find equation solutions, solve 2x-7=0 and 2x+7=0.
4x^{2}=10+39
Add 39 to both sides.
4x^{2}=49
Add 10 and 39 to get 49.
x^{2}=\frac{49}{4}
Divide both sides by 4.
x=\frac{7}{2} x=-\frac{7}{2}
Take the square root of both sides of the equation.
4x^{2}-39-10=0
Subtract 10 from both sides.
4x^{2}-49=0
Subtract 10 from -39 to get -49.
x=\frac{0±\sqrt{0^{2}-4\times 4\left(-49\right)}}{2\times 4}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and -49 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{0±\sqrt{-4\times 4\left(-49\right)}}{2\times 4}
Square 0.
x=\frac{0±\sqrt{-16\left(-49\right)}}{2\times 4}
Multiply -4 times 4.
x=\frac{0±\sqrt{784}}{2\times 4}
Multiply -16 times -49.
x=\frac{0±28}{2\times 4}
Take the square root of 784.
x=\frac{0±28}{8}
Multiply 2 times 4.
x=\frac{7}{2}
Now solve the equation x=\frac{0±28}{8} when ± is plus. Reduce the fraction \frac{28}{8} to lowest terms by extracting and canceling out 4.
x=-\frac{7}{2}
Now solve the equation x=\frac{0±28}{8} when ± is minus. Reduce the fraction \frac{-28}{8} to lowest terms by extracting and canceling out 4.
x=\frac{7}{2} x=-\frac{7}{2}
The equation is now solved.