Solve 70=10(1)+5x^2

$$70 = 10 ( 1 ) + 5 x ^ { 2 }$$

Solve for x

$$x=2\sqrt{3}\approx 3.464101615$$

$$x=-2\sqrt{3}\approx -3.464101615$$

Steps by Finding Square Root

Multiply 10 and 1 to get 10.

$$70=10+5x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$10+5x^{2}=70$$

Subtract 10 from both sides.

$$5x^{2}=70-10$$

Subtract 10 from 70 to get 60.

$$5x^{2}=60$$

Divide both sides by 5.

$$x^{2}=\frac{60}{5}$$

Divide 60 by 5 to get 12.

$$x^{2}=12$$

Take the square root of both sides of the equation.

$$x=2\sqrt{3} x=-2\sqrt{3}$$

Steps Using the Quadratic Formula

Multiply 10 and 1 to get 10.

$$70=10+5x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$10+5x^{2}=70$$

Subtract 70 from both sides.

$$10+5x^{2}-70=0$$

Subtract 70 from 10 to get -60.

$$-60+5x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$5x^{2}-60=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and -60 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 5\left(-60\right)}}{2\times 5}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 5\left(-60\right)}}{2\times 5}$$

Multiply -4 times 5.

$$x=\frac{0±\sqrt{-20\left(-60\right)}}{2\times 5}$$

Multiply -20 times -60.

$$x=\frac{0±\sqrt{1200}}{2\times 5}$$

Take the square root of 1200.

$$x=\frac{0±20\sqrt{3}}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{0±20\sqrt{3}}{10}$$

Now solve the equation x=\frac{0±20\sqrt{3}}{10} when ± is plus.

$$x=2\sqrt{3}$$

Now solve the equation x=\frac{0±20\sqrt{3}}{10} when ± is minus.

$$x=-2\sqrt{3}$$

The equation is now solved.

$$x=2\sqrt{3} x=-2\sqrt{3}$$