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Simplifying 37x + -2x2 = 100 Solving 37x + -2x2 = 100 Solving for variable 'x'. Reorder the terms: -100 + 37x + -2x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -100 + 37x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 50 + -18.5x + x2 = 0 Move the constant term to the right: Add '-50' to each side of the equation. 50 + -18.5x + -50 + x2 = 0 + -50 Reorder the terms: 50 + -50 + -18.5x + x2 = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -18.5x + x2 = 0 + -50 -18.5x + x2 = 0 + -50 Combine like terms: 0 + -50 = -50 -18.5x + x2 = -50 The x term is -18.5x. Take half its coefficient (-9.25). Square it (85.5625) and add it to both sides. Add '85.5625' to each side of the equation. -18.5x + 85.5625 + x2 = -50 + 85.5625 Reorder the terms: 85.5625 + -18.5x + x2 = -50 + 85.5625 Combine like terms: -50 + 85.5625 = 35.5625 85.5625 + -18.5x + x2 = 35.5625 Factor a perfect square on the left side: (x + -9.25)(x + -9.25) = 35.5625 Calculate the square root of the right side: 5.963430221 Break this problem into two subproblems by setting (x + -9.25) equal to 5.963430221 and -5.963430221.Subproblem 1
x + -9.25 = 5.963430221 Simplifying x + -9.25 = 5.963430221 Reorder the terms: -9.25 + x = 5.963430221 Solving -9.25 + x = 5.963430221 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.25' to each side of the equation. -9.25 + 9.25 + x = 5.963430221 + 9.25 Combine like terms: -9.25 + 9.25 = 0.00 0.00 + x = 5.963430221 + 9.25 x = 5.963430221 + 9.25 Combine like terms: 5.963430221 + 9.25 = 15.213430221 x = 15.213430221 Simplifying x = 15.213430221Subproblem 2
x + -9.25 = -5.963430221 Simplifying x + -9.25 = -5.963430221 Reorder the terms: -9.25 + x = -5.963430221 Solving -9.25 + x = -5.963430221 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.25' to each side of the equation. -9.25 + 9.25 + x = -5.963430221 + 9.25 Combine like terms: -9.25 + 9.25 = 0.00 0.00 + x = -5.963430221 + 9.25 x = -5.963430221 + 9.25 Combine like terms: -5.963430221 + 9.25 = 3.286569779 x = 3.286569779 Simplifying x = 3.286569779Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.213430221, 3.286569779}
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