Solve 7a^2-44a-35^2

$$7 a ^ { 2 } - 44 a - 35 ^ { 2 }$$

Factor

$$7\left(a-\frac{22-\sqrt{9059}}{7}\right)\left(a-\frac{\sqrt{9059}+22}{7}\right)$$

Steps Using the Quadratic Formula

Calculate 35 to the power of 2 and get 1225.

$$factor(7a^{2}-44a-1225)$$

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.

$$7a^{2}-44a-1225=0$$

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.

$$a=\frac{-\left(-44\right)±\sqrt{\left(-44\right)^{2}-4\times 7\left(-1225\right)}}{2\times 7}$$

Square -44.

$$a=\frac{-\left(-44\right)±\sqrt{1936-4\times 7\left(-1225\right)}}{2\times 7}$$

Multiply -4 times 7.

$$a=\frac{-\left(-44\right)±\sqrt{1936-28\left(-1225\right)}}{2\times 7}$$

Multiply -28 times -1225.

$$a=\frac{-\left(-44\right)±\sqrt{1936+34300}}{2\times 7}$$

Add 1936 to 34300.

$$a=\frac{-\left(-44\right)±\sqrt{36236}}{2\times 7}$$

Take the square root of 36236.

$$a=\frac{-\left(-44\right)±2\sqrt{9059}}{2\times 7}$$

The opposite of -44 is 44.

$$a=\frac{44±2\sqrt{9059}}{2\times 7}$$

Multiply 2 times 7.

$$a=\frac{44±2\sqrt{9059}}{14}$$

Now solve the equation a=\frac{44±2\sqrt{9059}}{14} when ± is plus. Add 44 to 2\sqrt{9059}.

$$a=\frac{2\sqrt{9059}+44}{14}$$

Divide 44+2\sqrt{9059} by 14.

$$a=\frac{\sqrt{9059}+22}{7}$$

Now solve the equation a=\frac{44±2\sqrt{9059}}{14} when ± is minus. Subtract 2\sqrt{9059} from 44.

$$a=\frac{44-2\sqrt{9059}}{14}$$

Divide 44-2\sqrt{9059} by 14.

$$a=\frac{22-\sqrt{9059}}{7}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{22+\sqrt{9059}}{7} for x_{1} and \frac{22-\sqrt{9059}}{7} for x_{2}.

$$7a^{2}-44a-1225=7\left(a-\frac{\sqrt{9059}+22}{7}\right)\left(a-\frac{22-\sqrt{9059}}{7}\right)$$

Evaluate

$$7a^{2}-44a-1225$$

Solution Steps

Calculate 35 to the power of 2 and get 1225.

$$7a^{2}-44a-1225$$