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Simplifying x2 + -13x = 130 Reorder the terms: -13x + x2 = 130 Solving -13x + x2 = 130 Solving for variable 'x'. Reorder the terms: -130 + -13x + x2 = 130 + -130 Combine like terms: 130 + -130 = 0 -130 + -13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '130' to each side of the equation. -130 + -13x + 130 + x2 = 0 + 130 Reorder the terms: -130 + 130 + -13x + x2 = 0 + 130 Combine like terms: -130 + 130 = 0 0 + -13x + x2 = 0 + 130 -13x + x2 = 0 + 130 Combine like terms: 0 + 130 = 130 -13x + x2 = 130 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 = 130 + 42.25 Reorder the terms: 42.25 + -13x + x2 = 130 + 42.25 Combine like terms: 130 + 42.25 = 172.25 42.25 + -13x + x2 = 172.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 172.25 Calculate the square root of the right side: 13.124404748 Break this problem into two subproblems by setting (x + -6.5) equal to 13.124404748 and -13.124404748.Subproblem 1
x + -6.5 = 13.124404748 Simplifying x + -6.5 = 13.124404748 Reorder the terms: -6.5 + x = 13.124404748 Solving -6.5 + x = 13.124404748 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 = 13.124404748 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 13.124404748 + 6.5 x = 13.124404748 + 6.5 Combine like terms: 13.124404748 + 6.5 = 19.624404748 x = 19.624404748 Simplifying x = 19.624404748Subproblem 2
x + -6.5 = -13.124404748 Simplifying x + -6.5 = -13.124404748 Reorder the terms: -6.5 + x = -13.124404748 Solving -6.5 + x = -13.124404748 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 = -13.124404748 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -13.124404748 + 6.5 x = -13.124404748 + 6.5 Combine like terms: -13.124404748 + 6.5 = -6.624404748 x = -6.624404748 Simplifying x = -6.624404748Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.624404748, -6.624404748}
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