Solve 2(x+5)*3(5*x)=10

$$2 ( x + 5 ) \cdot 3 ( 5 \cdot x ) = 10$$

Solve for x

$$x=\frac{\sqrt{237}}{6}-\frac{5}{2}\approx 0.06580072$$

$$x=-\frac{\sqrt{237}}{6}-\frac{5}{2}\approx -5.06580072$$

Steps Using the Quadratic Formula

Multiply 2 and 3 to get 6.

$$6\left(x+5\right)\times 5x=10$$

Multiply 6 and 5 to get 30.

$$30\left(x+5\right)x=10$$

Use the distributive property to multiply 30 by x+5.

$$\left(30x+150\right)x=10$$

Use the distributive property to multiply 30x+150 by x.

$$30x^{2}+150x=10$$

Subtract 10 from both sides.

$$30x^{2}+150x-10=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 30 for a, 150 for b, and -10 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-150±\sqrt{150^{2}-4\times 30\left(-10\right)}}{2\times 30}$$

Square 150.

$$x=\frac{-150±\sqrt{22500-4\times 30\left(-10\right)}}{2\times 30}$$

Multiply -4 times 30.

$$x=\frac{-150±\sqrt{22500-120\left(-10\right)}}{2\times 30}$$

Multiply -120 times -10.

$$x=\frac{-150±\sqrt{22500+1200}}{2\times 30}$$

Add 22500 to 1200.

$$x=\frac{-150±\sqrt{23700}}{2\times 30}$$

Take the square root of 23700.

$$x=\frac{-150±10\sqrt{237}}{2\times 30}$$

Multiply 2 times 30.

$$x=\frac{-150±10\sqrt{237}}{60}$$

Now solve the equation x=\frac{-150±10\sqrt{237}}{60} when ± is plus. Add -150 to 10\sqrt{237}.

$$x=\frac{10\sqrt{237}-150}{60}$$

Divide -150+10\sqrt{237} by 60.

$$x=\frac{\sqrt{237}}{6}-\frac{5}{2}$$

Now solve the equation x=\frac{-150±10\sqrt{237}}{60} when ± is minus. Subtract 10\sqrt{237} from -150.

$$x=\frac{-10\sqrt{237}-150}{60}$$

Divide -150-10\sqrt{237} by 60.

$$x=-\frac{\sqrt{237}}{6}-\frac{5}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{237}}{6}-\frac{5}{2} x=-\frac{\sqrt{237}}{6}-\frac{5}{2}$$

Steps for Completing the Square

Multiply 2 and 3 to get 6.

$$6\left(x+5\right)\times 5x=10$$

Multiply 6 and 5 to get 30.

$$30\left(x+5\right)x=10$$

Use the distributive property to multiply 30 by x+5.

$$\left(30x+150\right)x=10$$

Use the distributive property to multiply 30x+150 by x.

$$30x^{2}+150x=10$$

Divide both sides by 30.

$$\frac{30x^{2}+150x}{30}=\frac{10}{30}$$

Dividing by 30 undoes the multiplication by 30.

$$x^{2}+\frac{150}{30}x=\frac{10}{30}$$

Divide 150 by 30.

$$x^{2}+5x=\frac{10}{30}$$

Reduce the fraction \frac{10}{30} to lowest terms by extracting and canceling out 10.

$$x^{2}+5x=\frac{1}{3}$$

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

$$x^{2}+5x+\left(\frac{5}{2}\right)^{2}=\frac{1}{3}+\left(\frac{5}{2}\right)^{2}$$

Square \frac{5}{2} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+5x+\frac{25}{4}=\frac{1}{3}+\frac{25}{4}$$

Add \frac{1}{3} to \frac{25}{4} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}+5x+\frac{25}{4}=\frac{79}{12}$$

Factor x^{2}+5x+\frac{25}{4}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{5}{2}\right)^{2}=\frac{79}{12}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{5}{2}\right)^{2}}=\sqrt{\frac{79}{12}}$$

Simplify.

$$x+\frac{5}{2}=\frac{\sqrt{237}}{6} x+\frac{5}{2}=-\frac{\sqrt{237}}{6}$$

Subtract \frac{5}{2} from both sides of the equation.

$$x=\frac{\sqrt{237}}{6}-\frac{5}{2} x=-\frac{\sqrt{237}}{6}-\frac{5}{2}$$