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Simplifying x2 + 42.25 = -13x Reorder the terms: 42.25 + x2 = -13x Solving 42.25 + x2 = -13x Solving for variable 'x'. Reorder the terms: 42.25 + 13x + x2 = -13x + 13x Combine like terms: -13x + 13x = 0 42.25 + 13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-42.25' to each side of the equation. 42.25 + 13x + -42.25 + x2 = 0 + -42.25 Reorder the terms: 42.25 + -42.25 + 13x + x2 = 0 + -42.25 Combine like terms: 42.25 + -42.25 = 0.00 0.00 + 13x + x2 = 0 + -42.25 13x + x2 = 0 + -42.25 Combine like terms: 0 + -42.25 = -42.25 13x + x2 = -42.25 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 = -42.25 + 42.25 Reorder the terms: 42.25 + 13x + x2 = -42.25 + 42.25 Combine like terms: -42.25 + 42.25 = 0.00 42.25 + 13x + x2 = 0.00 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 0.00 Calculate the square root of the right side: 0.00 Break this problem into two subproblems by setting (x + 6.5) equal to 0.00 and 0.00.Subproblem 1
x + 6.5 = 0.00 Simplifying x + 6.5 = 0.00 Reorder the terms: 6.5 + x = 0.00 Solving 6.5 + x = 0.00 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 = 0.00 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 0.00 + -6.5 x = 0.00 + -6.5 Combine like terms: 0.00 + -6.5 = -6.5 x = -6.5 Simplifying x = -6.5Subproblem 2
x + 6.5 = 0.00 Simplifying x + 6.5 = 0.00 Reorder the terms: 6.5 + x = 0.00 Solving 6.5 + x = 0.00 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 = 0.00 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 0.00 + -6.5 x = 0.00 + -6.5 Combine like terms: 0.00 + -6.5 = -6.5 x = -6.5 Simplifying x = -6.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {-6.5, -6.5}
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