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Simplifying x2 + 15x + -20 = 0 Reorder the terms: -20 + 15x + x2 = 0 Solving -20 + 15x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + 15x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + 15x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 15x + x2 = 0 + 20 15x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 15x + x2 = 20 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = 20 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 20 + 56.25 Combine like terms: 20 + 56.25 = 76.25 56.25 + 15x + x2 = 76.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 76.25 Calculate the square root of the right side: 8.732124598 Break this problem into two subproblems by setting (x + 7.5) equal to 8.732124598 and -8.732124598.Subproblem 1
x + 7.5 = 8.732124598 Simplifying x + 7.5 = 8.732124598 Reorder the terms: 7.5 + x = 8.732124598 Solving 7.5 + x = 8.732124598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 8.732124598 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 8.732124598 + -7.5 x = 8.732124598 + -7.5 Combine like terms: 8.732124598 + -7.5 = 1.232124598 x = 1.232124598 Simplifying x = 1.232124598Subproblem 2
x + 7.5 = -8.732124598 Simplifying x + 7.5 = -8.732124598 Reorder the terms: 7.5 + x = -8.732124598 Solving 7.5 + x = -8.732124598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -8.732124598 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -8.732124598 + -7.5 x = -8.732124598 + -7.5 Combine like terms: -8.732124598 + -7.5 = -16.232124598 x = -16.232124598 Simplifying x = -16.232124598Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.232124598, -16.232124598}
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