Solve -4x^2-2x+8+6x-9

$$- 4 x ^ { 2 } - 2 x + 8 + 6 x - 9$$

Evaluate

$$-\left(2x-1\right)^{2}$$

Solution Steps

Combine -2x and 6x to get 4x.

$$-4x^{2}+4x+8-9$$

Subtract 9 from 8 to get -1.

$$-4x^{2}+4x-1$$

Factor

$$-\left(2x-1\right)^{2}$$

Solution Steps

Multiply and combine like terms.

$$-4x^{2}+4x-1$$

Factor the expression by grouping. First, the expression needs to be rewritten as -4x^{2}+ax+bx-1. To find a and b, set up a system to be solved.

$$a+b=4 ab=-4\left(-1\right)=4$$

Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. List all such integer pairs that give product 4.

$$1,4 2,2$$

Calculate the sum for each pair.

$$1+4=5 2+2=4$$

The solution is the pair that gives sum 4.

$$a=2 b=2$$

Rewrite -4x^{2}+4x-1 as \left(-4x^{2}+2x\right)+\left(2x-1\right).

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

Factor out -2x in -4x^{2}+2x.

$$-2x\left(2x-1\right)+2x-1$$

Factor out common term 2x-1 by using distributive property.

$$\left(2x-1\right)\left(-2x+1\right)$$