Solve 15*(1-x)*(1+x)+7x-3=0

$$15 \times (1-x) \times (1+x)+7x-3=0$$

Solve for x

$$x = \frac{\sqrt{769} + 7}{30} \approx 1.157694975$$

$$x=\frac{7-\sqrt{769}}{30}\approx -0.691028308$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 15 by 1-x.

$$\left(15-15x\right)\left(1+x\right)+7x-3=0$$

Use the distributive property to multiply 15-15x by 1+x and combine like terms.

$$15-15x^{2}+7x-3=0$$

Subtract 3 from 15 to get 12.

$$12-15x^{2}+7x=0$$

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.

$$-15x^{2}+7x+12=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -15 for a, 7 for b, and 12 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-7±\sqrt{7^{2}-4\left(-15\right)\times 12}}{2\left(-15\right)}$$

Square 7.

$$x=\frac{-7±\sqrt{49-4\left(-15\right)\times 12}}{2\left(-15\right)}$$

Multiply -4 times -15.

$$x=\frac{-7±\sqrt{49+60\times 12}}{2\left(-15\right)}$$

Multiply 60 times 12.

$$x=\frac{-7±\sqrt{49+720}}{2\left(-15\right)}$$

Add 49 to 720.

$$x=\frac{-7±\sqrt{769}}{2\left(-15\right)}$$

Multiply 2 times -15.

$$x=\frac{-7±\sqrt{769}}{-30}$$

Now solve the equation x=\frac{-7±\sqrt{769}}{-30} when ± is plus. Add -7 to \sqrt{769}.

$$x=\frac{\sqrt{769}-7}{-30}$$

Divide -7+\sqrt{769} by -30.

$$x=\frac{7-\sqrt{769}}{30}$$

Now solve the equation x=\frac{-7±\sqrt{769}}{-30} when ± is minus. Subtract \sqrt{769} from -7.

$$x=\frac{-\sqrt{769}-7}{-30}$$

Divide -7-\sqrt{769} by -30.

$$x=\frac{\sqrt{769}+7}{30}$$

The equation is now solved.

$$x=\frac{7-\sqrt{769}}{30} x=\frac{\sqrt{769}+7}{30}$$

Steps for Completing the Square

Use the distributive property to multiply 15 by 1-x.

$$\left(15-15x\right)\left(1+x\right)+7x-3=0$$

Use the distributive property to multiply 15-15x by 1+x and combine like terms.

$$15-15x^{2}+7x-3=0$$

Subtract 3 from 15 to get 12.

$$12-15x^{2}+7x=0$$

Subtract 12 from both sides. Anything subtracted from zero gives its negation.

$$-15x^{2}+7x=-12$$

Divide both sides by -15.

$$\frac{-15x^{2}+7x}{-15}=-\frac{12}{-15}$$

Dividing by -15 undoes the multiplication by -15.

$$x^{2}+\frac{7}{-15}x=-\frac{12}{-15}$$

Divide 7 by -15.

$$x^{2}-\frac{7}{15}x=-\frac{12}{-15}$$

Reduce the fraction \frac{-12}{-15} to lowest terms by extracting and canceling out 3.

$$x^{2}-\frac{7}{15}x=\frac{4}{5}$$

Divide -\frac{7}{15}, the coefficient of the x term, by 2 to get -\frac{7}{30}. Then add the square of -\frac{7}{30} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{7}{15}x+\left(-\frac{7}{30}\right)^{2}=\frac{4}{5}+\left(-\frac{7}{30}\right)^{2}$$

Square -\frac{7}{30} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{7}{15}x+\frac{49}{900}=\frac{4}{5}+\frac{49}{900}$$

Add \frac{4}{5} to \frac{49}{900} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}-\frac{7}{15}x+\frac{49}{900}=\frac{769}{900}$$

Factor x^{2}-\frac{7}{15}x+\frac{49}{900}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{7}{30}\right)^{2}=\frac{769}{900}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{7}{30}\right)^{2}}=\sqrt{\frac{769}{900}}$$

Simplify.

$$x-\frac{7}{30}=\frac{\sqrt{769}}{30} x-\frac{7}{30}=-\frac{\sqrt{769}}{30}$$

Add \frac{7}{30} to both sides of the equation.

$$x=\frac{\sqrt{769}+7}{30} x=\frac{7-\sqrt{769}}{30}$$