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Simplifying x + (x + 12) + (x + 12) * x = 68 Reorder the terms: x + (12 + x) + (x + 12) * x = 68 Remove parenthesis around (12 + x) x + 12 + x + (x + 12) * x = 68 Reorder the terms: x + 12 + x + (12 + x) * x = 68 Reorder the terms for easier multiplication: x + 12 + x + x(12 + x) = 68 x + 12 + x + (12 * x + x * x) = 68 x + 12 + x + (12x + x2) = 68 Reorder the terms: 12 + x + x + 12x + x2 = 68 Combine like terms: x + x = 2x 12 + 2x + 12x + x2 = 68 Combine like terms: 2x + 12x = 14x 12 + 14x + x2 = 68 Solving 12 + 14x + x2 = 68 Solving for variable 'x'. Reorder the terms: 12 + -68 + 14x + x2 = 68 + -68 Combine like terms: 12 + -68 = -56 -56 + 14x + x2 = 68 + -68 Combine like terms: 68 + -68 = 0 -56 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '56' to each side of the equation. -56 + 14x + 56 + x2 = 0 + 56 Reorder the terms: -56 + 56 + 14x + x2 = 0 + 56 Combine like terms: -56 + 56 = 0 0 + 14x + x2 = 0 + 56 14x + x2 = 0 + 56 Combine like terms: 0 + 56 = 56 14x + x2 = 56 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = 56 + 49 Reorder the terms: 49 + 14x + x2 = 56 + 49 Combine like terms: 56 + 49 = 105 49 + 14x + x2 = 105 Factor a perfect square on the left side: (x + 7)(x + 7) = 105 Calculate the square root of the right side: 10.246950766 Break this problem into two subproblems by setting (x + 7) equal to 10.246950766 and -10.246950766.Subproblem 1
x + 7 = 10.246950766 Simplifying x + 7 = 10.246950766 Reorder the terms: 7 + x = 10.246950766 Solving 7 + x = 10.246950766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 10.246950766 + -7 Combine like terms: 7 + -7 = 0 0 + x = 10.246950766 + -7 x = 10.246950766 + -7 Combine like terms: 10.246950766 + -7 = 3.246950766 x = 3.246950766 Simplifying x = 3.246950766Subproblem 2
x + 7 = -10.246950766 Simplifying x + 7 = -10.246950766 Reorder the terms: 7 + x = -10.246950766 Solving 7 + x = -10.246950766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -10.246950766 + -7 Combine like terms: 7 + -7 = 0 0 + x = -10.246950766 + -7 x = -10.246950766 + -7 Combine like terms: -10.246950766 + -7 = -17.246950766 x = -17.246950766 Simplifying x = -17.246950766Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.246950766, -17.246950766}
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