Solve 13*112=14*123-14x^2

$$13 \times 112 = 14 \times 123 - 14 x ^ { 2 }$$

Solve for x

$$x=\sqrt{19}\approx 4.358898944$$

$$x=-\sqrt{19}\approx -4.358898944$$

Steps by Finding Square Root

Multiply 13 and 112 to get 1456.

$$1456=14\times 123-14x^{2}$$

Multiply 14 and 123 to get 1722.

$$1456=1722-14x^{2}$$

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

$$1722-14x^{2}=1456$$

Subtract 1722 from both sides.

$$-14x^{2}=1456-1722$$

Subtract 1722 from 1456 to get -266.

$$-14x^{2}=-266$$

Divide both sides by -14.

$$x^{2}=\frac{-266}{-14}$$

Divide -266 by -14 to get 19.

$$x^{2}=19$$

Take the square root of both sides of the equation.

$$x=\sqrt{19} x=-\sqrt{19}$$

Steps Using the Quadratic Formula

Multiply 13 and 112 to get 1456.

$$1456=14\times 123-14x^{2}$$

Multiply 14 and 123 to get 1722.

$$1456=1722-14x^{2}$$

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

$$1722-14x^{2}=1456$$

Subtract 1456 from both sides.

$$1722-14x^{2}-1456=0$$

Subtract 1456 from 1722 to get 266.

$$266-14x^{2}=0$$

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.

$$-14x^{2}+266=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -14 for a, 0 for b, and 266 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-14\right)\times 266}}{2\left(-14\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-14\right)\times 266}}{2\left(-14\right)}$$

Multiply -4 times -14.

$$x=\frac{0±\sqrt{56\times 266}}{2\left(-14\right)}$$

Multiply 56 times 266.

$$x=\frac{0±\sqrt{14896}}{2\left(-14\right)}$$

Take the square root of 14896.

$$x=\frac{0±28\sqrt{19}}{2\left(-14\right)}$$

Multiply 2 times -14.

$$x=\frac{0±28\sqrt{19}}{-28}$$

Now solve the equation x=\frac{0±28\sqrt{19}}{-28} when ± is plus.

$$x=-\sqrt{19}$$

Now solve the equation x=\frac{0±28\sqrt{19}}{-28} when ± is minus.

$$x=\sqrt{19}$$

The equation is now solved.

$$x=-\sqrt{19} x=\sqrt{19}$$