Solve left(5xright)^2+6x+21=7(3-2x)

$${ \left(5x \right) }^{ 2 } +6x+21=7(3-2x)$$

Solve for x

$$x=-\frac{4}{5}=-0.8$$

$$x=0$$

Steps Using Factoring

Expand \left(5x\right)^{2}.

$$5^{2}x^{2}+6x+21=7\left(3-2x\right)$$

Calculate 5 to the power of 2 and get 25.

$$25x^{2}+6x+21=7\left(3-2x\right)$$

Use the distributive property to multiply 7 by 3-2x.

$$25x^{2}+6x+21=21-14x$$

Subtract 21 from both sides.

$$25x^{2}+6x+21-21=-14x$$

Subtract 21 from 21 to get 0.

$$25x^{2}+6x=-14x$$

Add 14x to both sides.

$$25x^{2}+6x+14x=0$$

Combine 6x and 14x to get 20x.

$$25x^{2}+20x=0$$

Factor out x.

$$x\left(25x+20\right)=0$$

To find equation solutions, solve x=0 and 25x+20=0.

$$x=0 x=-\frac{4}{5}$$

Steps Using the Quadratic Formula

Expand \left(5x\right)^{2}.

$$5^{2}x^{2}+6x+21=7\left(3-2x\right)$$

Calculate 5 to the power of 2 and get 25.

$$25x^{2}+6x+21=7\left(3-2x\right)$$

Use the distributive property to multiply 7 by 3-2x.

$$25x^{2}+6x+21=21-14x$$

Subtract 21 from both sides.

$$25x^{2}+6x+21-21=-14x$$

Subtract 21 from 21 to get 0.

$$25x^{2}+6x=-14x$$

Add 14x to both sides.

$$25x^{2}+6x+14x=0$$

Combine 6x and 14x to get 20x.

$$25x^{2}+20x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 25 for a, 20 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-20±\sqrt{20^{2}}}{2\times 25}$$

Take the square root of 20^{2}.

$$x=\frac{-20±20}{2\times 25}$$

Multiply 2 times 25.

$$x=\frac{-20±20}{50}$$

Now solve the equation x=\frac{-20±20}{50} when ± is plus. Add -20 to 20.

$$x=\frac{0}{50}$$

Divide 0 by 50.

$$x=0$$

Now solve the equation x=\frac{-20±20}{50} when ± is minus. Subtract 20 from -20.

$$x=-\frac{40}{50}$$

Reduce the fraction \frac{-40}{50} to lowest terms by extracting and canceling out 10.

$$x=-\frac{4}{5}$$

The equation is now solved.

$$x=0 x=-\frac{4}{5}$$

Steps for Completing the Square

Expand \left(5x\right)^{2}.

$$5^{2}x^{2}+6x+21=7\left(3-2x\right)$$

Calculate 5 to the power of 2 and get 25.

$$25x^{2}+6x+21=7\left(3-2x\right)$$

Use the distributive property to multiply 7 by 3-2x.

$$25x^{2}+6x+21=21-14x$$

Add 14x to both sides.

$$25x^{2}+6x+21+14x=21$$

Combine 6x and 14x to get 20x.

$$25x^{2}+20x+21=21$$

Subtract 21 from both sides.

$$25x^{2}+20x=21-21$$

Subtract 21 from 21 to get 0.

$$25x^{2}+20x=0$$

Divide both sides by 25.

$$\frac{25x^{2}+20x}{25}=\frac{0}{25}$$

Dividing by 25 undoes the multiplication by 25.

$$x^{2}+\frac{20}{25}x=\frac{0}{25}$$

Reduce the fraction \frac{20}{25} to lowest terms by extracting and canceling out 5.

$$x^{2}+\frac{4}{5}x=\frac{0}{25}$$

Divide 0 by 25.

$$x^{2}+\frac{4}{5}x=0$$

Divide \frac{4}{5}, the coefficient of the x term, by 2 to get \frac{2}{5}. Then add the square of \frac{2}{5} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

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

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

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

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

$$\left(x+\frac{2}{5}\right)^{2}=\frac{4}{25}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{2}{5}\right)^{2}}=\sqrt{\frac{4}{25}}$$

Simplify.

$$x+\frac{2}{5}=\frac{2}{5} x+\frac{2}{5}=-\frac{2}{5}$$

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

$$x=0 x=-\frac{4}{5}$$