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Simplifying x2 + -15x + -130 = 0 Reorder the terms: -130 + -15x + x2 = 0 Solving -130 + -15x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '130' to each side of the equation. -130 + -15x + 130 + x2 = 0 + 130 Reorder the terms: -130 + 130 + -15x + x2 = 0 + 130 Combine like terms: -130 + 130 = 0 0 + -15x + x2 = 0 + 130 -15x + x2 = 0 + 130 Combine like terms: 0 + 130 = 130 -15x + x2 = 130 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 = 130 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 130 + 56.25 Combine like terms: 130 + 56.25 = 186.25 56.25 + -15x + x2 = 186.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 186.25 Calculate the square root of the right side: 13.647344064 Break this problem into two subproblems by setting (x + -7.5) equal to 13.647344064 and -13.647344064.Subproblem 1
x + -7.5 = 13.647344064 Simplifying x + -7.5 = 13.647344064 Reorder the terms: -7.5 + x = 13.647344064 Solving -7.5 + x = 13.647344064 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 = 13.647344064 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 13.647344064 + 7.5 x = 13.647344064 + 7.5 Combine like terms: 13.647344064 + 7.5 = 21.147344064 x = 21.147344064 Simplifying x = 21.147344064Subproblem 2
x + -7.5 = -13.647344064 Simplifying x + -7.5 = -13.647344064 Reorder the terms: -7.5 + x = -13.647344064 Solving -7.5 + x = -13.647344064 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 = -13.647344064 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -13.647344064 + 7.5 x = -13.647344064 + 7.5 Combine like terms: -13.647344064 + 7.5 = -6.147344064 x = -6.147344064 Simplifying x = -6.147344064Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.147344064, -6.147344064}
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