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Simplifying x2 + (-13) * x + (-109.04) = 0 x2 + -13x + -109.04 = 0 Reorder the terms: -109.04 + -13x + x2 = 0 Solving -109.04 + -13x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '109.04' to each side of the equation. -109.04 + -13x + 109.04 + x2 = 0 + 109.04 Reorder the terms: -109.04 + 109.04 + -13x + x2 = 0 + 109.04 Combine like terms: -109.04 + 109.04 = 0.00 0.00 + -13x + x2 = 0 + 109.04 -13x + x2 = 0 + 109.04 Combine like terms: 0 + 109.04 = 109.04 -13x + x2 = 109.04 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 = 109.04 + 42.25 Reorder the terms: 42.25 + -13x + x2 = 109.04 + 42.25 Combine like terms: 109.04 + 42.25 = 151.29 42.25 + -13x + x2 = 151.29 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 151.29 Calculate the square root of the right side: 12.3 Break this problem into two subproblems by setting (x + -6.5) equal to 12.3 and -12.3.Subproblem 1
x + -6.5 = 12.3 Simplifying x + -6.5 = 12.3 Reorder the terms: -6.5 + x = 12.3 Solving -6.5 + x = 12.3 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 = 12.3 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 12.3 + 6.5 x = 12.3 + 6.5 Combine like terms: 12.3 + 6.5 = 18.8 x = 18.8 Simplifying x = 18.8Subproblem 2
x + -6.5 = -12.3 Simplifying x + -6.5 = -12.3 Reorder the terms: -6.5 + x = -12.3 Solving -6.5 + x = -12.3 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 = -12.3 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -12.3 + 6.5 x = -12.3 + 6.5 Combine like terms: -12.3 + 6.5 = -5.8 x = -5.8 Simplifying x = -5.8Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.8, -5.8}
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