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Simplifying 20x2 + 37x + -15 = 0 Reorder the terms: -15 + 37x + 20x2 = 0 Solving -15 + 37x + 20x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -0.75 + 1.85x + x2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + 1.85x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + 1.85x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + 1.85x + x2 = 0 + 0.75 1.85x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 1.85x + x2 = 0.75 The x term is 1.85x. Take half its coefficient (0.925). Square it (0.855625) and add it to both sides. Add '0.855625' to each side of the equation. 1.85x + 0.855625 + x2 = 0.75 + 0.855625 Reorder the terms: 0.855625 + 1.85x + x2 = 0.75 + 0.855625 Combine like terms: 0.75 + 0.855625 = 1.605625 0.855625 + 1.85x + x2 = 1.605625 Factor a perfect square on the left side: (x + 0.925)(x + 0.925) = 1.605625 Calculate the square root of the right side: 1.26713259 Break this problem into two subproblems by setting (x + 0.925) equal to 1.26713259 and -1.26713259.Subproblem 1
x + 0.925 = 1.26713259 Simplifying x + 0.925 = 1.26713259 Reorder the terms: 0.925 + x = 1.26713259 Solving 0.925 + x = 1.26713259 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.925' to each side of the equation. 0.925 + -0.925 + x = 1.26713259 + -0.925 Combine like terms: 0.925 + -0.925 = 0.000 0.000 + x = 1.26713259 + -0.925 x = 1.26713259 + -0.925 Combine like terms: 1.26713259 + -0.925 = 0.34213259 x = 0.34213259 Simplifying x = 0.34213259Subproblem 2
x + 0.925 = -1.26713259 Simplifying x + 0.925 = -1.26713259 Reorder the terms: 0.925 + x = -1.26713259 Solving 0.925 + x = -1.26713259 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.925' to each side of the equation. 0.925 + -0.925 + x = -1.26713259 + -0.925 Combine like terms: 0.925 + -0.925 = 0.000 0.000 + x = -1.26713259 + -0.925 x = -1.26713259 + -0.925 Combine like terms: -1.26713259 + -0.925 = -2.19213259 x = -2.19213259 Simplifying x = -2.19213259Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.34213259, -2.19213259}
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