Solve (2*x-1)*(x+8)-(x-1)*(x+1)=15*x

$$(2 \times x-1) \times (x+8)-(x-1) \times (x+1)=15 \times x$$

Solve for x

$$x=\sqrt{7}\approx 2.645751311$$

$$x=-\sqrt{7}\approx -2.645751311$$

Steps by Finding Square Root

Use the distributive property to multiply 2x-1 by x+8 and combine like terms.

$$2x^{2}+15x-8-\left(x-1\right)\left(x+1\right)=15x$$

Consider \left(x-1\right)\left(x+1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 1.

$$2x^{2}+15x-8-\left(x^{2}-1\right)=15x$$

To find the opposite of x^{2}-1, find the opposite of each term.

$$2x^{2}+15x-8-x^{2}+1=15x$$

Combine 2x^{2} and -x^{2} to get x^{2}.

$$x^{2}+15x-8+1=15x$$

Add -8 and 1 to get -7.

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

Subtract 15x from both sides.

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

Combine 15x and -15x to get 0.

$$x^{2}-7=0$$

Add 7 to both sides. Anything plus zero gives itself.

$$x^{2}=7$$

Take the square root of both sides of the equation.

$$x=\sqrt{7} x=-\sqrt{7}$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 2x-1 by x+8 and combine like terms.

$$2x^{2}+15x-8-\left(x-1\right)\left(x+1\right)=15x$$

Consider \left(x-1\right)\left(x+1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 1.

$$2x^{2}+15x-8-\left(x^{2}-1\right)=15x$$

To find the opposite of x^{2}-1, find the opposite of each term.

$$2x^{2}+15x-8-x^{2}+1=15x$$

Combine 2x^{2} and -x^{2} to get x^{2}.

$$x^{2}+15x-8+1=15x$$

Add -8 and 1 to get -7.

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

Subtract 15x from both sides.

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

Combine 15x and -15x to get 0.

$$x^{2}-7=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -7 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-7\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-7\right)}}{2}$$

Multiply -4 times -7.

$$x=\frac{0±\sqrt{28}}{2}$$

Take the square root of 28.

$$x=\frac{0±2\sqrt{7}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{7}}{2} when ± is plus.

$$x=\sqrt{7}$$

Now solve the equation x=\frac{0±2\sqrt{7}}{2} when ± is minus.

$$x=-\sqrt{7}$$

The equation is now solved.

$$x=\sqrt{7} x=-\sqrt{7}$$