Solve 36x^2-106=-sqrt{36}

$$36 x ^ { 2 } - 106 = - \sqrt { 36 }$$

Solve for x

$$x = \frac{5}{3} = 1\frac{2}{3} \approx 1.666666667$$

$$x = -\frac{5}{3} = -1\frac{2}{3} \approx -1.666666667$$

Steps Using Difference of Squares

Calculate the square root of 36 and get 6.

$$36x^{2}-106=-6$$

Add 6 to both sides.

$$36x^{2}-106+6=0$$

Add -106 and 6 to get -100.

$$36x^{2}-100=0$$

Divide both sides by 4.

$$9x^{2}-25=0$$

Consider 9x^{2}-25. Rewrite 9x^{2}-25 as \left(3x\right)^{2}-5^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(3x-5\right)\left(3x+5\right)=0$$

To find equation solutions, solve 3x-5=0 and 3x+5=0.

$$x=\frac{5}{3} x=-\frac{5}{3}$$

Steps by Finding Square Root

Calculate the square root of 36 and get 6.

$$36x^{2}-106=-6$$

Add 106 to both sides.

$$36x^{2}=-6+106$$

Add -6 and 106 to get 100.

$$36x^{2}=100$$

Divide both sides by 36.

$$x^{2}=\frac{100}{36}$$

Reduce the fraction \frac{100}{36} to lowest terms by extracting and canceling out 4.

$$x^{2}=\frac{25}{9}$$

Take the square root of both sides of the equation.

$$x=\frac{5}{3} x=-\frac{5}{3}$$

Steps Using the Quadratic Formula

Calculate the square root of 36 and get 6.

$$36x^{2}-106=-6$$

Add 6 to both sides.

$$36x^{2}-106+6=0$$

Add -106 and 6 to get -100.

$$36x^{2}-100=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 36 for a, 0 for b, and -100 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 36\left(-100\right)}}{2\times 36}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 36\left(-100\right)}}{2\times 36}$$

Multiply -4 times 36.

$$x=\frac{0±\sqrt{-144\left(-100\right)}}{2\times 36}$$

Multiply -144 times -100.

$$x=\frac{0±\sqrt{14400}}{2\times 36}$$

Take the square root of 14400.

$$x=\frac{0±120}{2\times 36}$$

Multiply 2 times 36.

$$x=\frac{0±120}{72}$$

Now solve the equation x=\frac{0±120}{72} when ± is plus. Reduce the fraction \frac{120}{72} to lowest terms by extracting and canceling out 24.

$$x=\frac{5}{3}$$

Now solve the equation x=\frac{0±120}{72} when ± is minus. Reduce the fraction \frac{-120}{72} to lowest terms by extracting and canceling out 24.

$$x=-\frac{5}{3}$$

The equation is now solved.

$$x=\frac{5}{3} x=-\frac{5}{3}$$