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Simplifying x2 = -13x + -5 Reorder the terms: x2 = -5 + -13x Solving x2 = -5 + -13x Solving for variable 'x'. Reorder the terms: 5 + 13x + x2 = -5 + -13x + 5 + 13x Reorder the terms: 5 + 13x + x2 = -5 + 5 + -13x + 13x Combine like terms: -5 + 5 = 0 5 + 13x + x2 = 0 + -13x + 13x 5 + 13x + x2 = -13x + 13x Combine like terms: -13x + 13x = 0 5 + 13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + 13x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + 13x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 13x + x2 = 0 + -5 13x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 13x + x2 = -5 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 = -5 + 42.25 Reorder the terms: 42.25 + 13x + x2 = -5 + 42.25 Combine like terms: -5 + 42.25 = 37.25 42.25 + 13x + x2 = 37.25 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 37.25 Calculate the square root of the right side: 6.103277808 Break this problem into two subproblems by setting (x + 6.5) equal to 6.103277808 and -6.103277808.Subproblem 1
x + 6.5 = 6.103277808 Simplifying x + 6.5 = 6.103277808 Reorder the terms: 6.5 + x = 6.103277808 Solving 6.5 + x = 6.103277808 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 = 6.103277808 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 6.103277808 + -6.5 x = 6.103277808 + -6.5 Combine like terms: 6.103277808 + -6.5 = -0.396722192 x = -0.396722192 Simplifying x = -0.396722192Subproblem 2
x + 6.5 = -6.103277808 Simplifying x + 6.5 = -6.103277808 Reorder the terms: 6.5 + x = -6.103277808 Solving 6.5 + x = -6.103277808 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 = -6.103277808 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -6.103277808 + -6.5 x = -6.103277808 + -6.5 Combine like terms: -6.103277808 + -6.5 = -12.603277808 x = -12.603277808 Simplifying x = -12.603277808Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.396722192, -12.603277808}
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