Solve 98/4+50-x^2/70=4/5

$$\frac{ \frac{ 98 }{ 4 } +50- { x }^{ 2 } }{ 70 } = \frac{ 4 }{ 5 }$$

Solve for x

$$x = \frac{\sqrt{74}}{2} \approx 4.301162634$$

$$x = -\frac{\sqrt{74}}{2} \approx -4.301162634$$

Steps by Finding Square Root

Multiply both sides by 70.

$$\frac{98}{4}+50-x^{2}=\frac{4}{5}\times 70$$

Reduce the fraction \frac{98}{4} to lowest terms by extracting and canceling out 2.

$$\frac{49}{2}+50-x^{2}=\frac{4}{5}\times 70$$

Add \frac{49}{2} and 50 to get \frac{149}{2}.

$$\frac{149}{2}-x^{2}=\frac{4}{5}\times 70$$

Multiply \frac{4}{5} and 70 to get 56.

$$\frac{149}{2}-x^{2}=56$$

Subtract \frac{149}{2} from both sides.

$$-x^{2}=56-\frac{149}{2}$$

Subtract \frac{149}{2} from 56 to get -\frac{37}{2}.

$$-x^{2}=-\frac{37}{2}$$

Divide both sides by -1.

$$x^{2}=\frac{-\frac{37}{2}}{-1}$$

Express \frac{-\frac{37}{2}}{-1} as a single fraction.

$$x^{2}=\frac{-37}{2\left(-1\right)}$$

Multiply 2 and -1 to get -2.

$$x^{2}=\frac{-37}{-2}$$

Fraction \frac{-37}{-2} can be simplified to \frac{37}{2} by removing the negative sign from both the numerator and the denominator.

$$x^{2}=\frac{37}{2}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{74}}{2} x=-\frac{\sqrt{74}}{2}$$

Steps Using the Quadratic Formula

Multiply both sides by 70.

$$\frac{98}{4}+50-x^{2}=\frac{4}{5}\times 70$$

Reduce the fraction \frac{98}{4} to lowest terms by extracting and canceling out 2.

$$\frac{49}{2}+50-x^{2}=\frac{4}{5}\times 70$$

Add \frac{49}{2} and 50 to get \frac{149}{2}.

$$\frac{149}{2}-x^{2}=\frac{4}{5}\times 70$$

Multiply \frac{4}{5} and 70 to get 56.

$$\frac{149}{2}-x^{2}=56$$

Subtract 56 from both sides.

$$\frac{149}{2}-x^{2}-56=0$$

Subtract 56 from \frac{149}{2} to get \frac{37}{2}.

$$\frac{37}{2}-x^{2}=0$$

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.

$$-x^{2}+\frac{37}{2}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and \frac{37}{2} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times \frac{37}{2}}}{2\left(-1\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\times \frac{37}{2}}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4\times \frac{37}{2}}}{2\left(-1\right)}$$

Multiply 4 times \frac{37}{2}.

$$x=\frac{0±\sqrt{74}}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{0±\sqrt{74}}{-2}$$

Now solve the equation x=\frac{0±\sqrt{74}}{-2} when ± is plus.

$$x=-\frac{\sqrt{74}}{2}$$

Now solve the equation x=\frac{0±\sqrt{74}}{-2} when ± is minus.

$$x=\frac{\sqrt{74}}{2}$$

The equation is now solved.

$$x=-\frac{\sqrt{74}}{2} x=\frac{\sqrt{74}}{2}$$