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Simplifying x2 + 13x + -30 = 16 Reorder the terms: -30 + 13x + x2 = 16 Solving -30 + 13x + x2 = 16 Solving for variable 'x'. Reorder the terms: -30 + -16 + 13x + x2 = 16 + -16 Combine like terms: -30 + -16 = -46 -46 + 13x + x2 = 16 + -16 Combine like terms: 16 + -16 = 0 -46 + 13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '46' to each side of the equation. -46 + 13x + 46 + x2 = 0 + 46 Reorder the terms: -46 + 46 + 13x + x2 = 0 + 46 Combine like terms: -46 + 46 = 0 0 + 13x + x2 = 0 + 46 13x + x2 = 0 + 46 Combine like terms: 0 + 46 = 46 13x + x2 = 46 The x term is 13x. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13x + 42.25 + x2 = 46 + 42.25 Reorder the terms: 42.25 + 13x + x2 = 46 + 42.25 Combine like terms: 46 + 42.25 = 88.25 42.25 + 13x + x2 = 88.25 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 88.25 Calculate the square root of the right side: 9.394147114 Break this problem into two subproblems by setting (x + 6.5) equal to 9.394147114 and -9.394147114.Subproblem 1
x + 6.5 = 9.394147114 Simplifying x + 6.5 = 9.394147114 Reorder the terms: 6.5 + x = 9.394147114 Solving 6.5 + x = 9.394147114 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = 9.394147114 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 9.394147114 + -6.5 x = 9.394147114 + -6.5 Combine like terms: 9.394147114 + -6.5 = 2.894147114 x = 2.894147114 Simplifying x = 2.894147114Subproblem 2
x + 6.5 = -9.394147114 Simplifying x + 6.5 = -9.394147114 Reorder the terms: 6.5 + x = -9.394147114 Solving 6.5 + x = -9.394147114 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = -9.394147114 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -9.394147114 + -6.5 x = -9.394147114 + -6.5 Combine like terms: -9.394147114 + -6.5 = -15.894147114 x = -15.894147114 Simplifying x = -15.894147114Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.894147114, -15.894147114}
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