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Simplifying 140 = x2 + 8x Reorder the terms: 140 = 8x + x2 Solving 140 = 8x + x2 Solving for variable 'x'. Reorder the terms: 140 + -8x + -1x2 = 8x + -8x + x2 + -1x2 Combine like terms: 8x + -8x = 0 140 + -8x + -1x2 = 0 + x2 + -1x2 140 + -8x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 140 + -8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -140 + 8x + x2 = 0 Move the constant term to the right: Add '140' to each side of the equation. -140 + 8x + 140 + x2 = 0 + 140 Reorder the terms: -140 + 140 + 8x + x2 = 0 + 140 Combine like terms: -140 + 140 = 0 0 + 8x + x2 = 0 + 140 8x + x2 = 0 + 140 Combine like terms: 0 + 140 = 140 8x + x2 = 140 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 140 + 16 Reorder the terms: 16 + 8x + x2 = 140 + 16 Combine like terms: 140 + 16 = 156 16 + 8x + x2 = 156 Factor a perfect square on the left side: (x + 4)(x + 4) = 156 Calculate the square root of the right side: 12.489995997 Break this problem into two subproblems by setting (x + 4) equal to 12.489995997 and -12.489995997.Subproblem 1
x + 4 = 12.489995997 Simplifying x + 4 = 12.489995997 Reorder the terms: 4 + x = 12.489995997 Solving 4 + x = 12.489995997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 12.489995997 + -4 Combine like terms: 4 + -4 = 0 0 + x = 12.489995997 + -4 x = 12.489995997 + -4 Combine like terms: 12.489995997 + -4 = 8.489995997 x = 8.489995997 Simplifying x = 8.489995997Subproblem 2
x + 4 = -12.489995997 Simplifying x + 4 = -12.489995997 Reorder the terms: 4 + x = -12.489995997 Solving 4 + x = -12.489995997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -12.489995997 + -4 Combine like terms: 4 + -4 = 0 0 + x = -12.489995997 + -4 x = -12.489995997 + -4 Combine like terms: -12.489995997 + -4 = -16.489995997 x = -16.489995997 Simplifying x = -16.489995997Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.489995997, -16.489995997}
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