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Simplifying x = (100 + -1x)(30 + 4x) Multiply (100 + -1x) * (30 + 4x) x = (100(30 + 4x) + -1x * (30 + 4x)) x = ((30 * 100 + 4x * 100) + -1x * (30 + 4x)) x = ((3000 + 400x) + -1x * (30 + 4x)) x = (3000 + 400x + (30 * -1x + 4x * -1x)) x = (3000 + 400x + (-30x + -4x2)) Combine like terms: 400x + -30x = 370x x = (3000 + 370x + -4x2) Solving x = 3000 + 370x + -4x2 Solving for variable 'x'. Reorder the terms: -3000 + x + -370x + 4x2 = 3000 + 370x + -4x2 + -3000 + -370x + 4x2 Combine like terms: x + -370x = -369x -3000 + -369x + 4x2 = 3000 + 370x + -4x2 + -3000 + -370x + 4x2 Reorder the terms: -3000 + -369x + 4x2 = 3000 + -3000 + 370x + -370x + -4x2 + 4x2 Combine like terms: 3000 + -3000 = 0 -3000 + -369x + 4x2 = 0 + 370x + -370x + -4x2 + 4x2 -3000 + -369x + 4x2 = 370x + -370x + -4x2 + 4x2 Combine like terms: 370x + -370x = 0 -3000 + -369x + 4x2 = 0 + -4x2 + 4x2 -3000 + -369x + 4x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 -3000 + -369x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -750 + -92.25x + x2 = 0 Move the constant term to the right: Add '750' to each side of the equation. -750 + -92.25x + 750 + x2 = 0 + 750 Reorder the terms: -750 + 750 + -92.25x + x2 = 0 + 750 Combine like terms: -750 + 750 = 0 0 + -92.25x + x2 = 0 + 750 -92.25x + x2 = 0 + 750 Combine like terms: 0 + 750 = 750 -92.25x + x2 = 750 The x term is -92.25x. Take half its coefficient (-46.125). Square it (2127.515625) and add it to both sides. Add '2127.515625' to each side of the equation. -92.25x + 2127.515625 + x2 = 750 + 2127.515625 Reorder the terms: 2127.515625 + -92.25x + x2 = 750 + 2127.515625 Combine like terms: 750 + 2127.515625 = 2877.515625 2127.515625 + -92.25x + x2 = 2877.515625 Factor a perfect square on the left side: (x + -46.125)(x + -46.125) = 2877.515625 Calculate the square root of the right side: 53.642479669 Break this problem into two subproblems by setting (x + -46.125) equal to 53.642479669 and -53.642479669.Subproblem 1
x + -46.125 = 53.642479669 Simplifying x + -46.125 = 53.642479669 Reorder the terms: -46.125 + x = 53.642479669 Solving -46.125 + x = 53.642479669 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '46.125' to each side of the equation. -46.125 + 46.125 + x = 53.642479669 + 46.125 Combine like terms: -46.125 + 46.125 = 0.000 0.000 + x = 53.642479669 + 46.125 x = 53.642479669 + 46.125 Combine like terms: 53.642479669 + 46.125 = 99.767479669 x = 99.767479669 Simplifying x = 99.767479669Subproblem 2
x + -46.125 = -53.642479669 Simplifying x + -46.125 = -53.642479669 Reorder the terms: -46.125 + x = -53.642479669 Solving -46.125 + x = -53.642479669 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '46.125' to each side of the equation. -46.125 + 46.125 + x = -53.642479669 + 46.125 Combine like terms: -46.125 + 46.125 = 0.000 0.000 + x = -53.642479669 + 46.125 x = -53.642479669 + 46.125 Combine like terms: -53.642479669 + 46.125 = -7.517479669 x = -7.517479669 Simplifying x = -7.517479669Solution
The solution to the problem is based on the solutions from the subproblems. x = {99.767479669, -7.517479669}
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