Solve x^2-6x+-3^2

$${ x }^{ 2 } -6x+ { -3 }^{ 2 }$$

Factor

$$\left(x-3\right)^{2}$$

Solution Steps

Multiply and combine like terms.

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

Factor the expression by grouping. First, the expression needs to be rewritten as x^{2}+ax+bx+9. To find a and b, set up a system to be solved.

$$a+b=-6 ab=1\times 9=9$$

Since ab is positive, a and b have the same sign. Since a+b is negative, a and b are both negative. List all such integer pairs that give product 9.

$$-1,-9 -3,-3$$

Calculate the sum for each pair.

$$-1-9=-10 -3-3=-6$$

The solution is the pair that gives sum -6.

$$a=-3 b=-3$$

Rewrite x^{2}-6x+9 as \left(x^{2}-3x\right)+\left(-3x+9\right).

$$\left(x^{2}-3x\right)+\left(-3x+9\right)$$

Factor out x in the first and -3 in the second group.

$$x\left(x-3\right)-3\left(x-3\right)$$

Factor out common term x-3 by using distributive property.

$$\left(x-3\right)\left(x-3\right)$$

Rewrite as a binomial square.

$$\left(x-3\right)^{2}$$

Evaluate

$$\left(x-3\right)^{2}$$

Solution Steps

Calculate -3 to the power of 2 and get 9.

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