Question

I need help with this problem x^2=7x+17 step by step using the “completing the square” method

Answer 1

`x^2=7x+17\\x^2-7x-17=0\\D=(-7)^2-4*(-17)=117\\\\x_1=(7+√(117) )/(2) =(7+3√(13) )/(2) \\x_2=(7-√(117) )/(2) =(7-3√(13) )/(2)`

`Answer: \\x_1=(7+3√(13) )/(2) \\\\x_2=(7-3√(13) )/(2)`

P.S. Hello from Russia

Answer 2

x =
`(7-3√(13))/(2)` x=
`(7-3√(13))/(2)`

Explanation:

Step 1: Subtract 7x on both sides

`x^(2) = 7x + 17`

Step 2: Subtract 17 on both sides

`x^(2) - 7x = 17\\x^(2) -7x - 17 = 0`

Solve with the quadratic formula:

`\quad x_(1,\:2)=(-b\pm √(b^2-4ac))/(2a)`

`\mathrm{For\:}\quad a=1,\:b=-7,\:c=-17:\quad x_(1,\:2)=(-\left(-7\right)\pm √(\left(-7\right)^2-4\cdot \:1\left(-17\right)))/(2\cdot \:1)`

`(-\left(-7\right)+√(\left(-7\right)^2-4\cdot \:1\cdot \left(-17\right)))/(2\cdot \:1)`

=
`(7+√(117))/(2\cdot \:1)`

=
`(7+√(117))/(2)`

=
`(7+3√(13))/(2)`

`(-\left(-7\right)-√(\left(-7\right)^2-4\cdot \:1\cdot \left(-17\right)))/(2\cdot \:1)`

=
`(7-√(117))/(2\cdot \:1)`

=
`(7-√(117))/(2)`

=
`(7-3√(13))/(2)`

x =
`(7-3√(13))/(2)` x=
`(7-3√(13))/(2)`