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Simplifying x2 + -1(76.01) * x + 9.24 = 0 Multiply -1 * 76.01 x2 + -76.01x + 9.24 = 0 Reorder the terms: 9.24 + -76.01x + x2 = 0 Solving 9.24 + -76.01x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-9.24' to each side of the equation. 9.24 + -76.01x + -9.24 + x2 = 0 + -9.24 Reorder the terms: 9.24 + -9.24 + -76.01x + x2 = 0 + -9.24 Combine like terms: 9.24 + -9.24 = 0.00 0.00 + -76.01x + x2 = 0 + -9.24 -76.01x + x2 = 0 + -9.24 Combine like terms: 0 + -9.24 = -9.24 -76.01x + x2 = -9.24 The x term is -76.01x. Take half its coefficient (-38.005). Square it (1444.380025) and add it to both sides. Add '1444.380025' to each side of the equation. -76.01x + 1444.380025 + x2 = -9.24 + 1444.380025 Reorder the terms: 1444.380025 + -76.01x + x2 = -9.24 + 1444.380025 Combine like terms: -9.24 + 1444.380025 = 1435.140025 1444.380025 + -76.01x + x2 = 1435.140025 Factor a perfect square on the left side: (x + -38.005)(x + -38.005) = 1435.140025 Calculate the square root of the right side: 37.883242008 Break this problem into two subproblems by setting (x + -38.005) equal to 37.883242008 and -37.883242008.Subproblem 1
x + -38.005 = 37.883242008 Simplifying x + -38.005 = 37.883242008 Reorder the terms: -38.005 + x = 37.883242008 Solving -38.005 + x = 37.883242008 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '38.005' to each side of the equation. -38.005 + 38.005 + x = 37.883242008 + 38.005 Combine like terms: -38.005 + 38.005 = 0.000 0.000 + x = 37.883242008 + 38.005 x = 37.883242008 + 38.005 Combine like terms: 37.883242008 + 38.005 = 75.888242008 x = 75.888242008 Simplifying x = 75.888242008Subproblem 2
x + -38.005 = -37.883242008 Simplifying x + -38.005 = -37.883242008 Reorder the terms: -38.005 + x = -37.883242008 Solving -38.005 + x = -37.883242008 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '38.005' to each side of the equation. -38.005 + 38.005 + x = -37.883242008 + 38.005 Combine like terms: -38.005 + 38.005 = 0.000 0.000 + x = -37.883242008 + 38.005 x = -37.883242008 + 38.005 Combine like terms: -37.883242008 + 38.005 = 0.121757992 x = 0.121757992 Simplifying x = 0.121757992Solution
The solution to the problem is based on the solutions from the subproblems. x = {75.888242008, 0.121757992}
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