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Simplifying 0 = x2 + 35x + 60 Reorder the terms: 0 = 60 + 35x + x2 Solving 0 = 60 + 35x + x2 Solving for variable 'x'. Combine like terms: 0 + -60 = -60 -60 + -35x + -1x2 = 60 + 35x + x2 + -60 + -35x + -1x2 Reorder the terms: -60 + -35x + -1x2 = 60 + -60 + 35x + -35x + x2 + -1x2 Combine like terms: 60 + -60 = 0 -60 + -35x + -1x2 = 0 + 35x + -35x + x2 + -1x2 -60 + -35x + -1x2 = 35x + -35x + x2 + -1x2 Combine like terms: 35x + -35x = 0 -60 + -35x + -1x2 = 0 + x2 + -1x2 -60 + -35x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -60 + -35x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(60 + 35x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(60 + 35x + x2)' equal to zero and attempt to solve: Simplifying 60 + 35x + x2 = 0 Solving 60 + 35x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-60' to each side of the equation. 60 + 35x + -60 + x2 = 0 + -60 Reorder the terms: 60 + -60 + 35x + x2 = 0 + -60 Combine like terms: 60 + -60 = 0 0 + 35x + x2 = 0 + -60 35x + x2 = 0 + -60 Combine like terms: 0 + -60 = -60 35x + x2 = -60 The x term is 35x. Take half its coefficient (17.5). Square it (306.25) and add it to both sides. Add '306.25' to each side of the equation. 35x + 306.25 + x2 = -60 + 306.25 Reorder the terms: 306.25 + 35x + x2 = -60 + 306.25 Combine like terms: -60 + 306.25 = 246.25 306.25 + 35x + x2 = 246.25 Factor a perfect square on the left side: (x + 17.5)(x + 17.5) = 246.25 Calculate the square root of the right side: 15.692354826 Break this problem into two subproblems by setting (x + 17.5) equal to 15.692354826 and -15.692354826.Subproblem 1
x + 17.5 = 15.692354826 Simplifying x + 17.5 = 15.692354826 Reorder the terms: 17.5 + x = 15.692354826 Solving 17.5 + x = 15.692354826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.5' to each side of the equation. 17.5 + -17.5 + x = 15.692354826 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = 15.692354826 + -17.5 x = 15.692354826 + -17.5 Combine like terms: 15.692354826 + -17.5 = -1.807645174 x = -1.807645174 Simplifying x = -1.807645174Subproblem 2
x + 17.5 = -15.692354826 Simplifying x + 17.5 = -15.692354826 Reorder the terms: 17.5 + x = -15.692354826 Solving 17.5 + x = -15.692354826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.5' to each side of the equation. 17.5 + -17.5 + x = -15.692354826 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = -15.692354826 + -17.5 x = -15.692354826 + -17.5 Combine like terms: -15.692354826 + -17.5 = -33.192354826 x = -33.192354826 Simplifying x = -33.192354826Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.807645174, -33.192354826}Solution
x = {-1.807645174, -33.192354826}
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