Solve 3-1/4x^2+x+2/2-x=-1

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

Solve for x

$$x=2\sqrt{7}\approx 5.291502622$$

$$x=-2\sqrt{7}\approx -5.291502622$$

Steps by Finding Square Root

Variable x cannot be equal to 2 since division by zero is not defined. Multiply both sides of the equation by -x+2.

$$3-\frac{1}{4}x^{2}+x+2=-\left(-x+2\right)$$

Add 3 and 2 to get 5.

$$5-\frac{1}{4}x^{2}+x=-\left(-x+2\right)$$

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

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

Subtract x from both sides.

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

Combine x and -x to get 0.

$$5-\frac{1}{4}x^{2}=-2$$

Subtract 5 from both sides.

$$-\frac{1}{4}x^{2}=-2-5$$

Subtract 5 from -2 to get -7.

$$-\frac{1}{4}x^{2}=-7$$

Multiply both sides by -4, the reciprocal of -\frac{1}{4}.

$$x^{2}=-7\left(-4\right)$$

Multiply -7 and -4 to get 28.

$$x^{2}=28$$

Take the square root of both sides of the equation.

$$x=2\sqrt{7} x=-2\sqrt{7}$$

Steps Using the Quadratic Formula

Variable x cannot be equal to 2 since division by zero is not defined. Multiply both sides of the equation by -x+2.

$$3-\frac{1}{4}x^{2}+x+2=-\left(-x+2\right)$$

Add 3 and 2 to get 5.

$$5-\frac{1}{4}x^{2}+x=-\left(-x+2\right)$$

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

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

Subtract x from both sides.

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

Combine x and -x to get 0.

$$5-\frac{1}{4}x^{2}=-2$$

Add 2 to both sides.

$$5-\frac{1}{4}x^{2}+2=0$$

Add 5 and 2 to get 7.

$$7-\frac{1}{4}x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-\frac{1}{4}x^{2}+7=0$$

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

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{1}{4}\right)\times 7}}{2\left(-\frac{1}{4}\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{1}{4}\right)\times 7}}{2\left(-\frac{1}{4}\right)}$$

Multiply -4 times -\frac{1}{4}.

$$x=\frac{0±\sqrt{7}}{2\left(-\frac{1}{4}\right)}$$

Multiply 2 times -\frac{1}{4}.

$$x=\frac{0±\sqrt{7}}{-\frac{1}{2}}$$

Now solve the equation x=\frac{0±\sqrt{7}}{-\frac{1}{2}} when ± is plus.

$$x=-2\sqrt{7}$$

Now solve the equation x=\frac{0±\sqrt{7}}{-\frac{1}{2}} when ± is minus.

$$x=2\sqrt{7}$$

The equation is now solved.

$$x=-2\sqrt{7} x=2\sqrt{7}$$