Solve -4x^2+7x-3x^2+8

$$- 4 x ^ { 2 } + 7 x - 3 x ^ { 2 } + 8$$

Factor

$$-7\left(x-\left(-\frac{\sqrt{273}}{14}+\frac{1}{2}\right)\right)\left(x-\left(\frac{\sqrt{273}}{14}+\frac{1}{2}\right)\right)$$

Steps Using the Quadratic Formula

Combine -4x^{2} and -3x^{2} to get -7x^{2}.

$$factor(-7x^{2}+7x+8)$$

Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.

$$-7x^{2}+7x+8=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$x=\frac{-7±\sqrt{7^{2}-4\left(-7\right)\times 8}}{2\left(-7\right)}$$

Square 7.

$$x=\frac{-7±\sqrt{49-4\left(-7\right)\times 8}}{2\left(-7\right)}$$

Multiply -4 times -7.

$$x=\frac{-7±\sqrt{49+28\times 8}}{2\left(-7\right)}$$

Multiply 28 times 8.

$$x=\frac{-7±\sqrt{49+224}}{2\left(-7\right)}$$

Add 49 to 224.

$$x=\frac{-7±\sqrt{273}}{2\left(-7\right)}$$

Multiply 2 times -7.

$$x=\frac{-7±\sqrt{273}}{-14}$$

Now solve the equation x=\frac{-7±\sqrt{273}}{-14} when ± is plus. Add -7 to \sqrt{273}.

$$x=\frac{\sqrt{273}-7}{-14}$$

Divide -7+\sqrt{273} by -14.

$$x=-\frac{\sqrt{273}}{14}+\frac{1}{2}$$

Now solve the equation x=\frac{-7±\sqrt{273}}{-14} when ± is minus. Subtract \sqrt{273} from -7.

$$x=\frac{-\sqrt{273}-7}{-14}$$

Divide -7-\sqrt{273} by -14.

$$x=\frac{\sqrt{273}}{14}+\frac{1}{2}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{1}{2}-\frac{\sqrt{273}}{14} for x_{1} and \frac{1}{2}+\frac{\sqrt{273}}{14} for x_{2}.

$$-7x^{2}+7x+8=-7\left(x-\left(-\frac{\sqrt{273}}{14}+\frac{1}{2}\right)\right)\left(x-\left(\frac{\sqrt{273}}{14}+\frac{1}{2}\right)\right)$$

Evaluate

$$8+7x-7x^{2}$$

Solution Steps

Combine -4x^{2} and -3x^{2} to get -7x^{2}.

$$-7x^{2}+7x+8$$