Solve 2*15.8=100-y/(y)^2

$$2 \times 15.8 = \frac { 100 - y } { ( y ) ^ { 2 } }$$

Solve for y

$$y = \frac{5 \sqrt{12641} - 5}{316} \approx 1.76316775$$

$$y=\frac{-5\sqrt{12641}-5}{316}\approx -1.79481332$$

Steps Using the Quadratic Formula

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by y^{2}.

$$2\times 15.8y^{2}=100-y$$

Multiply 2 and 15.8 to get 31.6.

$$31.6y^{2}=100-y$$

Subtract 100 from both sides.

$$31.6y^{2}-100=-y$$

Add y to both sides.

$$31.6y^{2}-100+y=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$31.6y^{2}+y-100=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 31.6 for a, 1 for b, and -100 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{-1±\sqrt{1^{2}-4\times 31.6\left(-100\right)}}{2\times 31.6}$$

Square 1.

$$y=\frac{-1±\sqrt{1-4\times 31.6\left(-100\right)}}{2\times 31.6}$$

Multiply -4 times 31.6.

$$y=\frac{-1±\sqrt{1-126.4\left(-100\right)}}{2\times 31.6}$$

Multiply -126.4 times -100.

$$y=\frac{-1±\sqrt{1+12640}}{2\times 31.6}$$

Add 1 to 12640.

$$y=\frac{-1±\sqrt{12641}}{2\times 31.6}$$

Multiply 2 times 31.6.

$$y=\frac{-1±\sqrt{12641}}{63.2}$$

Now solve the equation y=\frac{-1±\sqrt{12641}}{63.2} when ± is plus. Add -1 to \sqrt{12641}.

$$y=\frac{\sqrt{12641}-1}{63.2}$$

Divide -1+\sqrt{12641} by 63.2 by multiplying -1+\sqrt{12641} by the reciprocal of 63.2.

$$y=\frac{5\sqrt{12641}-5}{316}$$

Now solve the equation y=\frac{-1±\sqrt{12641}}{63.2} when ± is minus. Subtract \sqrt{12641} from -1.

$$y=\frac{-\sqrt{12641}-1}{63.2}$$

Divide -1-\sqrt{12641} by 63.2 by multiplying -1-\sqrt{12641} by the reciprocal of 63.2.

$$y=\frac{-5\sqrt{12641}-5}{316}$$

The equation is now solved.

$$y=\frac{5\sqrt{12641}-5}{316} y=\frac{-5\sqrt{12641}-5}{316}$$

Steps for Completing the Square

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by y^{2}.

$$2\times 15.8y^{2}=100-y$$

Multiply 2 and 15.8 to get 31.6.

$$31.6y^{2}=100-y$$

Add y to both sides.

$$31.6y^{2}+y=100$$

Divide both sides of the equation by 31.6, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{31.6y^{2}+y}{31.6}=\frac{100}{31.6}$$

Dividing by 31.6 undoes the multiplication by 31.6.

$$y^{2}+\frac{1}{31.6}y=\frac{100}{31.6}$$

Divide 1 by 31.6 by multiplying 1 by the reciprocal of 31.6.

$$y^{2}+\frac{5}{158}y=\frac{100}{31.6}$$

Divide 100 by 31.6 by multiplying 100 by the reciprocal of 31.6.

$$y^{2}+\frac{5}{158}y=\frac{250}{79}$$

Divide \frac{5}{158}, the coefficient of the x term, by 2 to get \frac{5}{316}. Then add the square of \frac{5}{316} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$y^{2}+\frac{5}{158}y+\frac{5}{316}^{2}=\frac{250}{79}+\frac{5}{316}^{2}$$

Square \frac{5}{316} by squaring both the numerator and the denominator of the fraction.

$$y^{2}+\frac{5}{158}y+\frac{25}{99856}=\frac{250}{79}+\frac{25}{99856}$$

Add \frac{250}{79} to \frac{25}{99856} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$y^{2}+\frac{5}{158}y+\frac{25}{99856}=\frac{316025}{99856}$$

Factor y^{2}+\frac{5}{158}y+\frac{25}{99856}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(y+\frac{5}{316}\right)^{2}=\frac{316025}{99856}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(y+\frac{5}{316}\right)^{2}}=\sqrt{\frac{316025}{99856}}$$

Simplify.

$$y+\frac{5}{316}=\frac{5\sqrt{12641}}{316} y+\frac{5}{316}=-\frac{5\sqrt{12641}}{316}$$

Subtract \frac{5}{316} from both sides of the equation.

$$y=\frac{5\sqrt{12641}-5}{316} y=\frac{-5\sqrt{12641}-5}{316}$$