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Simplifying 147x + -49 = 3x2 + -1x2 Reorder the terms: -49 + 147x = 3x2 + -1x2 Combine like terms: 3x2 + -1x2 = 2x2 -49 + 147x = 2x2 Solving -49 + 147x = 2x2 Solving for variable 'x'. Combine like terms: 2x2 + -2x2 = 0 -49 + 147x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 24.5 + -73.5x + x2 = 0 Move the constant term to the right: Add '-24.5' to each side of the equation. 24.5 + -73.5x + -24.5 + x2 = 0 + -24.5 Reorder the terms: 24.5 + -24.5 + -73.5x + x2 = 0 + -24.5 Combine like terms: 24.5 + -24.5 = 0.0 0.0 + -73.5x + x2 = 0 + -24.5 -73.5x + x2 = 0 + -24.5 Combine like terms: 0 + -24.5 = -24.5 -73.5x + x2 = -24.5 The x term is -73.5x. Take half its coefficient (-36.75). Square it (1350.5625) and add it to both sides. Add '1350.5625' to each side of the equation. -73.5x + 1350.5625 + x2 = -24.5 + 1350.5625 Reorder the terms: 1350.5625 + -73.5x + x2 = -24.5 + 1350.5625 Combine like terms: -24.5 + 1350.5625 = 1326.0625 1350.5625 + -73.5x + x2 = 1326.0625 Factor a perfect square on the left side: (x + -36.75)(x + -36.75) = 1326.0625 Calculate the square root of the right side: 36.415141082 Break this problem into two subproblems by setting (x + -36.75) equal to 36.415141082 and -36.415141082.Subproblem 1
x + -36.75 = 36.415141082 Simplifying x + -36.75 = 36.415141082 Reorder the terms: -36.75 + x = 36.415141082 Solving -36.75 + x = 36.415141082 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '36.75' to each side of the equation. -36.75 + 36.75 + x = 36.415141082 + 36.75 Combine like terms: -36.75 + 36.75 = 0.00 0.00 + x = 36.415141082 + 36.75 x = 36.415141082 + 36.75 Combine like terms: 36.415141082 + 36.75 = 73.165141082 x = 73.165141082 Simplifying x = 73.165141082Subproblem 2
x + -36.75 = -36.415141082 Simplifying x + -36.75 = -36.415141082 Reorder the terms: -36.75 + x = -36.415141082 Solving -36.75 + x = -36.415141082 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '36.75' to each side of the equation. -36.75 + 36.75 + x = -36.415141082 + 36.75 Combine like terms: -36.75 + 36.75 = 0.00 0.00 + x = -36.415141082 + 36.75 x = -36.415141082 + 36.75 Combine like terms: -36.415141082 + 36.75 = 0.334858918 x = 0.334858918 Simplifying x = 0.334858918Solution
The solution to the problem is based on the solutions from the subproblems. x = {73.165141082, 0.334858918}
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