type the correct answer in each box. use numerals instead of words. consider the quadratic equation…

type the correct answer in each box. use numerals instead of words. consider the quadratic equation $x^{2}+10x + 27 = 0$. completing the square leads to the equivalent equation $(x+square)^{2}=square$.

type the correct answer in each box. use numerals instead of words. consider the quadratic equation $x^{2}+10x + 27 = 0$. completing the square leads to the equivalent equation $(x+square)^{2}=square$.

Answer

Explanation:

Step1: Recall the formula for completing the square

For a quadratic equation of the form $x^{2}+bx + c=0$, to complete the square we use $(x+\frac{b}{2})^{2}=x^{2}+bx+\frac{b^{2}}{4}$. In the given equation $x^{2}+10x + 27=0$, where $b = 10$.

Step2: Rewrite the left - hand side of the equation

First, for the $x^{2}+10x$ part, we know that $x^{2}+10x=(x + 5)^{2}-25$ (since $\frac{b}{2}=\frac{10}{2}=5$ and $(x + 5)^{2}=x^{2}+10x + 25$). So the original equation $x^{2}+10x+27 = 0$ can be rewritten as $(x + 5)^{2}-25+27=0$.

Step3: Simplify the equation

Simplify $(x + 5)^{2}-25+27=0$ to get $(x + 5)^{2}+2=0$, then $(x + 5)^{2}=-2$.

Answer:

5, - 2