Solve x^2-74x^2+5+x-1

$$x ^ { 2 } - 74 x ^ { 2 } + 5 + x - 1$$

Evaluate

$$4+x-73x^{2}$$

Solution Steps

Combine x^{2} and -74x^{2} to get -73x^{2}.

$$-73x^{2}+5+x-1$$

Subtract 1 from 5 to get 4.

$$-73x^{2}+4+x$$

Factor

$$-73\left(x-\frac{1-\sqrt{1169}}{146}\right)\left(x-\frac{\sqrt{1169}+1}{146}\right)$$

Steps Using the Quadratic Formula

Combine x^{2} and -74x^{2} to get -73x^{2}.

$$factor(-73x^{2}+5+x-1)$$

Subtract 1 from 5 to get 4.

$$factor(-73x^{2}+4+x)$$

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.

$$-73x^{2}+x+4=0$$

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.

$$x=\frac{-1±\sqrt{1^{2}-4\left(-73\right)\times 4}}{2\left(-73\right)}$$

Square 1.

$$x=\frac{-1±\sqrt{1-4\left(-73\right)\times 4}}{2\left(-73\right)}$$

Multiply -4 times -73.

$$x=\frac{-1±\sqrt{1+292\times 4}}{2\left(-73\right)}$$

Multiply 292 times 4.

$$x=\frac{-1±\sqrt{1+1168}}{2\left(-73\right)}$$

Add 1 to 1168.

$$x=\frac{-1±\sqrt{1169}}{2\left(-73\right)}$$

Multiply 2 times -73.

$$x=\frac{-1±\sqrt{1169}}{-146}$$

Now solve the equation x=\frac{-1±\sqrt{1169}}{-146} when ± is plus. Add -1 to \sqrt{1169}.

$$x=\frac{\sqrt{1169}-1}{-146}$$

Divide -1+\sqrt{1169} by -146.

$$x=\frac{1-\sqrt{1169}}{146}$$

Now solve the equation x=\frac{-1±\sqrt{1169}}{-146} when ± is minus. Subtract \sqrt{1169} from -1.

$$x=\frac{-\sqrt{1169}-1}{-146}$$

Divide -1-\sqrt{1169} by -146.

$$x=\frac{\sqrt{1169}+1}{146}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{1-\sqrt{1169}}{146} for x_{1} and \frac{1+\sqrt{1169}}{146} for x_{2}.

$$-73x^{2}+x+4=-73\left(x-\frac{1-\sqrt{1169}}{146}\right)\left(x-\frac{\sqrt{1169}+1}{146}\right)$$