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Simplifying x(x + 6) = 140 Reorder the terms: x(6 + x) = 140 (6 * x + x * x) = 140 (6x + x2) = 140 Solving 6x + x2 = 140 Solving for variable 'x'. Reorder the terms: -140 + 6x + x2 = 140 + -140 Combine like terms: 140 + -140 = 0 -140 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '140' to each side of the equation. -140 + 6x + 140 + x2 = 0 + 140 Reorder the terms: -140 + 140 + 6x + x2 = 0 + 140 Combine like terms: -140 + 140 = 0 0 + 6x + x2 = 0 + 140 6x + x2 = 0 + 140 Combine like terms: 0 + 140 = 140 6x + x2 = 140 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 = 140 + 9 Reorder the terms: 9 + 6x + x2 = 140 + 9 Combine like terms: 140 + 9 = 149 9 + 6x + x2 = 149 Factor a perfect square on the left side: (x + 3)(x + 3) = 149 Calculate the square root of the right side: 12.206555616 Break this problem into two subproblems by setting (x + 3) equal to 12.206555616 and -12.206555616.Subproblem 1
x + 3 = 12.206555616 Simplifying x + 3 = 12.206555616 Reorder the terms: 3 + x = 12.206555616 Solving 3 + x = 12.206555616 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 = 12.206555616 + -3 Combine like terms: 3 + -3 = 0 0 + x = 12.206555616 + -3 x = 12.206555616 + -3 Combine like terms: 12.206555616 + -3 = 9.206555616 x = 9.206555616 Simplifying x = 9.206555616Subproblem 2
x + 3 = -12.206555616 Simplifying x + 3 = -12.206555616 Reorder the terms: 3 + x = -12.206555616 Solving 3 + x = -12.206555616 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 = -12.206555616 + -3 Combine like terms: 3 + -3 = 0 0 + x = -12.206555616 + -3 x = -12.206555616 + -3 Combine like terms: -12.206555616 + -3 = -15.206555616 x = -15.206555616 Simplifying x = -15.206555616Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.206555616, -15.206555616}
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