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Simplifying 114 = (x)(x + 2)(7) Reorder the terms: 114 = x(2 + x)(7) Reorder the terms for easier multiplication: 114 = 7x(2 + x) 114 = (2 * 7x + x * 7x) 114 = (14x + 7x2) Solving 114 = 14x + 7x2 Solving for variable 'x'. Reorder the terms: 114 + -14x + -7x2 = 14x + -14x + 7x2 + -7x2 Combine like terms: 14x + -14x = 0 114 + -14x + -7x2 = 0 + 7x2 + -7x2 114 + -14x + -7x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 114 + -14x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -16.28571429 + 2x + x2 = 0 Move the constant term to the right: Add '16.28571429' to each side of the equation. -16.28571429 + 2x + 16.28571429 + x2 = 0 + 16.28571429 Reorder the terms: -16.28571429 + 16.28571429 + 2x + x2 = 0 + 16.28571429 Combine like terms: -16.28571429 + 16.28571429 = 0.00000000 0.00000000 + 2x + x2 = 0 + 16.28571429 2x + x2 = 0 + 16.28571429 Combine like terms: 0 + 16.28571429 = 16.28571429 2x + x2 = 16.28571429 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 16.28571429 + 1 Reorder the terms: 1 + 2x + x2 = 16.28571429 + 1 Combine like terms: 16.28571429 + 1 = 17.28571429 1 + 2x + x2 = 17.28571429 Factor a perfect square on the left side: (x + 1)(x + 1) = 17.28571429 Calculate the square root of the right side: 4.157609204 Break this problem into two subproblems by setting (x + 1) equal to 4.157609204 and -4.157609204.Subproblem 1
x + 1 = 4.157609204 Simplifying x + 1 = 4.157609204 Reorder the terms: 1 + x = 4.157609204 Solving 1 + x = 4.157609204 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 4.157609204 + -1 Combine like terms: 1 + -1 = 0 0 + x = 4.157609204 + -1 x = 4.157609204 + -1 Combine like terms: 4.157609204 + -1 = 3.157609204 x = 3.157609204 Simplifying x = 3.157609204Subproblem 2
x + 1 = -4.157609204 Simplifying x + 1 = -4.157609204 Reorder the terms: 1 + x = -4.157609204 Solving 1 + x = -4.157609204 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -4.157609204 + -1 Combine like terms: 1 + -1 = 0 0 + x = -4.157609204 + -1 x = -4.157609204 + -1 Combine like terms: -4.157609204 + -1 = -5.157609204 x = -5.157609204 Simplifying x = -5.157609204Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.157609204, -5.157609204}
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