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Simplifying x * x + 6x = 1 Multiply x * x 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 1
x + 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 = 0.16227766Subproblem 2
x + 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 = -6.16227766Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.16227766, -6.16227766}
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