Solve 25+36-x^2/60=7/10

$$\frac { 25 + 36 - x ^ { 2 } } { 60 } = \frac { 7 } { 10 }$$

Solve for x

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

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

Steps by Finding Square Root

Multiply both sides by 60.

$$25+36-x^{2}=\frac{7}{10}\times 60$$

Add 25 and 36 to get 61.

$$61-x^{2}=\frac{7}{10}\times 60$$

Multiply \frac{7}{10} and 60 to get 42.

$$61-x^{2}=42$$

Subtract 61 from both sides.

$$-x^{2}=42-61$$

Subtract 61 from 42 to get -19.

$$-x^{2}=-19$$

Divide both sides by -1.

$$x^{2}=\frac{-19}{-1}$$

Fraction \frac{-19}{-1} can be simplified to 19 by removing the negative sign from both the numerator and the denominator.

$$x^{2}=19$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Multiply both sides by 60.

$$25+36-x^{2}=\frac{7}{10}\times 60$$

Add 25 and 36 to get 61.

$$61-x^{2}=\frac{7}{10}\times 60$$

Multiply \frac{7}{10} and 60 to get 42.

$$61-x^{2}=42$$

Subtract 42 from both sides.

$$61-x^{2}-42=0$$

Subtract 42 from 61 to get 19.

$$19-x^{2}=0$$

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.

$$-x^{2}+19=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and 19 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 19}}{2\left(-1\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\times 19}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4\times 19}}{2\left(-1\right)}$$

Multiply 4 times 19.

$$x=\frac{0±\sqrt{76}}{2\left(-1\right)}$$

Take the square root of 76.

$$x=\frac{0±2\sqrt{19}}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{0±2\sqrt{19}}{-2}$$

Now solve the equation x=\frac{0±2\sqrt{19}}{-2} when ± is plus.

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

Now solve the equation x=\frac{0±2\sqrt{19}}{-2} when ± is minus.

$$x=\sqrt{19}$$

The equation is now solved.

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