Solve 2*(x-2)-(2x-7)=-(x-2)*(x+2)

$$2 \cdot ( x - 2 ) - ( 2 x - 7 ) = - ( x - 2 ) \cdot ( x + 2 )$$

Solve for x

$$x=-1$$

$$x=1$$

Steps by Finding Square Root

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

$$2x-4-\left(2x-7\right)=\left(-\left(x-2\right)\right)\left(x+2\right)$$

To find the opposite of 2x-7, find the opposite of each term.

$$2x-4-2x-\left(-7\right)=\left(-\left(x-2\right)\right)\left(x+2\right)$$

The opposite of -7 is 7.

$$2x-4-2x+7=\left(-\left(x-2\right)\right)\left(x+2\right)$$

Combine 2x and -2x to get 0.

$$-4+7=\left(-\left(x-2\right)\right)\left(x+2\right)$$

Add -4 and 7 to get 3.

$$3=\left(-\left(x-2\right)\right)\left(x+2\right)$$

To find the opposite of x-2, find the opposite of each term.

$$3=\left(-x-\left(-2\right)\right)\left(x+2\right)$$

The opposite of -2 is 2.

$$3=\left(-x+2\right)\left(x+2\right)$$

Apply the distributive property by multiplying each term of -x+2 by each term of x+2.

$$3=-x^{2}-2x+2x+4$$

Combine -2x and 2x to get 0.

$$3=-x^{2}+4$$

Swap sides so that all variable terms are on the left hand side.

$$-x^{2}+4=3$$

Subtract 4 from both sides.

$$-x^{2}=3-4$$

Subtract 4 from 3 to get -1.

$$-x^{2}=-1$$

Divide both sides by -1.

$$x^{2}=\frac{-1}{-1}$$

Divide -1 by -1 to get 1.

$$x^{2}=1$$

Take the square root of both sides of the equation.

$$x=1 x=-1$$

Steps Using the Quadratic Formula

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

$$2x-4-\left(2x-7\right)=\left(-\left(x-2\right)\right)\left(x+2\right)$$

To find the opposite of 2x-7, find the opposite of each term.

$$2x-4-2x-\left(-7\right)=\left(-\left(x-2\right)\right)\left(x+2\right)$$

The opposite of -7 is 7.

$$2x-4-2x+7=\left(-\left(x-2\right)\right)\left(x+2\right)$$

Combine 2x and -2x to get 0.

$$-4+7=\left(-\left(x-2\right)\right)\left(x+2\right)$$

Add -4 and 7 to get 3.

$$3=\left(-\left(x-2\right)\right)\left(x+2\right)$$

To find the opposite of x-2, find the opposite of each term.

$$3=\left(-x-\left(-2\right)\right)\left(x+2\right)$$

The opposite of -2 is 2.

$$3=\left(-x+2\right)\left(x+2\right)$$

Apply the distributive property by multiplying each term of -x+2 by each term of x+2.

$$3=-x^{2}-2x+2x+4$$

Combine -2x and 2x to get 0.

$$3=-x^{2}+4$$

Swap sides so that all variable terms are on the left hand side.

$$-x^{2}+4=3$$

Subtract 3 from both sides.

$$-x^{2}+4-3=0$$

Subtract 3 from 4 to get 1.

$$-x^{2}+1=0$$

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

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)}}{2\left(-1\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4}}{2\left(-1\right)}$$

Take the square root of 4.

$$x=\frac{0±2}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{0±2}{-2}$$

Now solve the equation x=\frac{0±2}{-2} when ± is plus. Divide 2 by -2.

$$x=-1$$

Now solve the equation x=\frac{0±2}{-2} when ± is minus. Divide -2 by -2.

$$x=1$$

The equation is now solved.

$$x=-1 x=1$$