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Simplifying x2 + 3.8x + -60.61 = 0 Reorder the terms: -60.61 + 3.8x + x2 = 0 Solving -60.61 + 3.8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '60.61' to each side of the equation. -60.61 + 3.8x + 60.61 + x2 = 0 + 60.61 Reorder the terms: -60.61 + 60.61 + 3.8x + x2 = 0 + 60.61 Combine like terms: -60.61 + 60.61 = 0.00 0.00 + 3.8x + x2 = 0 + 60.61 3.8x + x2 = 0 + 60.61 Combine like terms: 0 + 60.61 = 60.61 3.8x + x2 = 60.61 The x term is 3.8x. Take half its coefficient (1.9). Square it (3.61) and add it to both sides. Add '3.61' to each side of the equation. 3.8x + 3.61 + x2 = 60.61 + 3.61 Reorder the terms: 3.61 + 3.8x + x2 = 60.61 + 3.61 Combine like terms: 60.61 + 3.61 = 64.22 3.61 + 3.8x + x2 = 64.22 Factor a perfect square on the left side: (x + 1.9)(x + 1.9) = 64.22 Calculate the square root of the right side: 8.013738204 Break this problem into two subproblems by setting (x + 1.9) equal to 8.013738204 and -8.013738204.Subproblem 1
x + 1.9 = 8.013738204 Simplifying x + 1.9 = 8.013738204 Reorder the terms: 1.9 + x = 8.013738204 Solving 1.9 + x = 8.013738204 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.9' to each side of the equation. 1.9 + -1.9 + x = 8.013738204 + -1.9 Combine like terms: 1.9 + -1.9 = 0.0 0.0 + x = 8.013738204 + -1.9 x = 8.013738204 + -1.9 Combine like terms: 8.013738204 + -1.9 = 6.113738204 x = 6.113738204 Simplifying x = 6.113738204Subproblem 2
x + 1.9 = -8.013738204 Simplifying x + 1.9 = -8.013738204 Reorder the terms: 1.9 + x = -8.013738204 Solving 1.9 + x = -8.013738204 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.9' to each side of the equation. 1.9 + -1.9 + x = -8.013738204 + -1.9 Combine like terms: 1.9 + -1.9 = 0.0 0.0 + x = -8.013738204 + -1.9 x = -8.013738204 + -1.9 Combine like terms: -8.013738204 + -1.9 = -9.913738204 x = -9.913738204 Simplifying x = -9.913738204Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.113738204, -9.913738204}
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