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Simplifying 32x2 + 25x + -60 = 0 Reorder the terms: -60 + 25x + 32x2 = 0 Solving -60 + 25x + 32x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. -1.875 + 0.78125x + x2 = 0 Move the constant term to the right: Add '1.875' to each side of the equation. -1.875 + 0.78125x + 1.875 + x2 = 0 + 1.875 Reorder the terms: -1.875 + 1.875 + 0.78125x + x2 = 0 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + 0.78125x + x2 = 0 + 1.875 0.78125x + x2 = 0 + 1.875 Combine like terms: 0 + 1.875 = 1.875 0.78125x + x2 = 1.875 The x term is 0.78125x. Take half its coefficient (0.390625). Square it (0.1525878906) and add it to both sides. Add '0.1525878906' to each side of the equation. 0.78125x + 0.1525878906 + x2 = 1.875 + 0.1525878906 Reorder the terms: 0.1525878906 + 0.78125x + x2 = 1.875 + 0.1525878906 Combine like terms: 1.875 + 0.1525878906 = 2.0275878906 0.1525878906 + 0.78125x + x2 = 2.0275878906 Factor a perfect square on the left side: (x + 0.390625)(x + 0.390625) = 2.0275878906 Calculate the square root of the right side: 1.423933949 Break this problem into two subproblems by setting (x + 0.390625) equal to 1.423933949 and -1.423933949.Subproblem 1
x + 0.390625 = 1.423933949 Simplifying x + 0.390625 = 1.423933949 Reorder the terms: 0.390625 + x = 1.423933949 Solving 0.390625 + x = 1.423933949 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.390625' to each side of the equation. 0.390625 + -0.390625 + x = 1.423933949 + -0.390625 Combine like terms: 0.390625 + -0.390625 = 0.000000 0.000000 + x = 1.423933949 + -0.390625 x = 1.423933949 + -0.390625 Combine like terms: 1.423933949 + -0.390625 = 1.033308949 x = 1.033308949 Simplifying x = 1.033308949Subproblem 2
x + 0.390625 = -1.423933949 Simplifying x + 0.390625 = -1.423933949 Reorder the terms: 0.390625 + x = -1.423933949 Solving 0.390625 + x = -1.423933949 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.390625' to each side of the equation. 0.390625 + -0.390625 + x = -1.423933949 + -0.390625 Combine like terms: 0.390625 + -0.390625 = 0.000000 0.000000 + x = -1.423933949 + -0.390625 x = -1.423933949 + -0.390625 Combine like terms: -1.423933949 + -0.390625 = -1.814558949 x = -1.814558949 Simplifying x = -1.814558949Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.033308949, -1.814558949}
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