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Simplifying (x + 4)(140 + -1x) = 150 Reorder the terms: (4 + x)(140 + -1x) = 150 Multiply (4 + x) * (140 + -1x) (4(140 + -1x) + x(140 + -1x)) = 150 ((140 * 4 + -1x * 4) + x(140 + -1x)) = 150 ((560 + -4x) + x(140 + -1x)) = 150 (560 + -4x + (140 * x + -1x * x)) = 150 (560 + -4x + (140x + -1x2)) = 150 Combine like terms: -4x + 140x = 136x (560 + 136x + -1x2) = 150 Solving 560 + 136x + -1x2 = 150 Solving for variable 'x'. Reorder the terms: 560 + -150 + 136x + -1x2 = 150 + -150 Combine like terms: 560 + -150 = 410 410 + 136x + -1x2 = 150 + -150 Combine like terms: 150 + -150 = 0 410 + 136x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -410 + -136x + x2 = 0 Move the constant term to the right: Add '410' to each side of the equation. -410 + -136x + 410 + x2 = 0 + 410 Reorder the terms: -410 + 410 + -136x + x2 = 0 + 410 Combine like terms: -410 + 410 = 0 0 + -136x + x2 = 0 + 410 -136x + x2 = 0 + 410 Combine like terms: 0 + 410 = 410 -136x + x2 = 410 The x term is -136x. Take half its coefficient (-68). Square it (4624) and add it to both sides. Add '4624' to each side of the equation. -136x + 4624 + x2 = 410 + 4624 Reorder the terms: 4624 + -136x + x2 = 410 + 4624 Combine like terms: 410 + 4624 = 5034 4624 + -136x + x2 = 5034 Factor a perfect square on the left side: (x + -68)(x + -68) = 5034 Calculate the square root of the right side: 70.9506871 Break this problem into two subproblems by setting (x + -68) equal to 70.9506871 and -70.9506871.Subproblem 1
x + -68 = 70.9506871 Simplifying x + -68 = 70.9506871 Reorder the terms: -68 + x = 70.9506871 Solving -68 + x = 70.9506871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '68' to each side of the equation. -68 + 68 + x = 70.9506871 + 68 Combine like terms: -68 + 68 = 0 0 + x = 70.9506871 + 68 x = 70.9506871 + 68 Combine like terms: 70.9506871 + 68 = 138.9506871 x = 138.9506871 Simplifying x = 138.9506871Subproblem 2
x + -68 = -70.9506871 Simplifying x + -68 = -70.9506871 Reorder the terms: -68 + x = -70.9506871 Solving -68 + x = -70.9506871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '68' to each side of the equation. -68 + 68 + x = -70.9506871 + 68 Combine like terms: -68 + 68 = 0 0 + x = -70.9506871 + 68 x = -70.9506871 + 68 Combine like terms: -70.9506871 + 68 = -2.9506871 x = -2.9506871 Simplifying x = -2.9506871Solution
The solution to the problem is based on the solutions from the subproblems. x = {138.9506871, -2.9506871}
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