Question

Solve using completing the square methodx^2-6x=7

Answer 1

Answer:

x = -1, or x = 7

Explanations:

The given equation is:

`x^2-6x\text{ = 7}`

The given equation is of the form:

`\begin{gathered} ax^2+bx\text{ = c} \\ \text{where a = 1, b = -6, c = 7} \end{gathered}`
`\text{Add }((|b|)/(2))^2\text{ to both sides of the equation}`
`((|b|)/(2))^2=\text{ (}(6)/(2))^2=3^2`

Therefore, the equation becomes:

`\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}`

Simpliifying the above equation further:

`(x-3)^2\text{ = 16}`

Find the square root of both sides of the equation

`\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}`

Therefore, x = -1, or x = 7