Question

This question says solve the equation by completing the square. can anyone help me please? i'm not sure how to do this.
here is the problem:
x^2+6x=1

Answer 1

Simplifying
x2 + 6x = 1

Reorder the terms:
6x + x2 = 1

Solving
6x + x2 = 1

Solving for variable 'x'.

Reorder the terms:
-1 + 6x + x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 6x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 6x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 6x + x2 = 0 + 1
6x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
6x + x2 = 1

The x term is 6x. Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 1 + 9

Reorder the terms:
9 + 6x + x2 = 1 + 9

Combine like terms: 1 + 9 = 10
9 + 6x + x2 = 10

Factor a perfect square on the left side:
(x + 3)(x + 3) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting
(x + 3) equal to 3.16227766 and -3.16227766.

Subproblem 1x + 3 = 3.16227766

Simplifying
x + 3 = 3.16227766

Reorder the terms:
3 + x = 3.16227766

Solving
3 + x = 3.16227766

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + x = 3.16227766 + -3

Combine like terms: 3 + -3 = 0
0 + x = 3.16227766 + -3
x = 3.16227766 + -3

Combine like terms: 3.16227766 + -3 = 0.16227766
x = 0.16227766

Simplifying
x = 0.16227766

Subproblem 2x + 3 = -3.16227766

Simplifying
x + 3 = -3.16227766

Reorder the terms:
3 + x = -3.16227766

Solving
3 + x = -3.16227766

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + x = -3.16227766 + -3

Combine like terms: 3 + -3 = 0
0 + x = -3.16227766 + -3
x = -3.16227766 + -3

Combine like terms: -3.16227766 + -3 = -6.16227766
x = -6.16227766

Simplifying
x = -6.16227766

SolutionThe solution to the problem is based on the solutions
from the subproblems.
x = {0.16227766, -6.16227766}

Answer 2

kay thank you. that helped me.

Answer 3

Np.