x = -1, or x = 7
Explanations:The given equation is:
[tex]x^2-6x\text{ = 7}[/tex]The given equation is of the form:
[tex]\begin{gathered} ax^2+bx\text{ = c} \\ \text{where a = 1, b = -6, c = 7} \end{gathered}[/tex][tex]\text{Add }(\frac{|b|}{2})^2\text{ to both sides of the equation}[/tex][tex](\frac{|b|}{2})^2=\text{ (}\frac{6}{2})^2=3^2[/tex]Therefore, the equation becomes:
[tex]\begin{gathered} x^2-6x+3^2=7+3^2 \\ x^2-6x+3^2\text{ = 7+9} \\ x^2-6x+3^2\text{ =16} \end{gathered}[/tex]Simpliifying the above equation further:
[tex](x-3)^2\text{ = 16}[/tex]Find the square root of both sides of the equation
[tex]\begin{gathered} \sqrt[]{(x-3)^2\text{ }}\text{ = }\pm\sqrt[]{16} \\ x\text{ - 3 = }\pm4 \\ x\text{ - 3 = 4 or x -3 = -4} \\ For\text{ x -3 = 4} \\ x\text{ = 4 + 3} \\ x\text{ = 7} \\ \text{For x - 3 = -4} \\ x\text{ = -4 + 3} \\ x\text{ = -1} \end{gathered}[/tex]Therefore, x = -1, or x = 7
