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Simplifying 4x2 + 36x = 180 Reorder the terms: 36x + 4x2 = 180 Solving 36x + 4x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + 36x + 4x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + 36x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-45 + 9x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-45 + 9x + x2)' equal to zero and attempt to solve: Simplifying -45 + 9x + x2 = 0 Solving -45 + 9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + 9x + 45 + x2 = 0 + 45 Reorder the terms: -45 + 45 + 9x + x2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + 9x + x2 = 0 + 45 9x + x2 = 0 + 45 Combine like terms: 0 + 45 = 45 9x + x2 = 45 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 45 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 45 + 20.25 Combine like terms: 45 + 20.25 = 65.25 20.25 + 9x + x2 = 65.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 65.25 Calculate the square root of the right side: 8.077747211 Break this problem into two subproblems by setting (x + 4.5) equal to 8.077747211 and -8.077747211.Subproblem 1
x + 4.5 = 8.077747211 Simplifying x + 4.5 = 8.077747211 Reorder the terms: 4.5 + x = 8.077747211 Solving 4.5 + x = 8.077747211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 8.077747211 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 8.077747211 + -4.5 x = 8.077747211 + -4.5 Combine like terms: 8.077747211 + -4.5 = 3.577747211 x = 3.577747211 Simplifying x = 3.577747211Subproblem 2
x + 4.5 = -8.077747211 Simplifying x + 4.5 = -8.077747211 Reorder the terms: 4.5 + x = -8.077747211 Solving 4.5 + x = -8.077747211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -8.077747211 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -8.077747211 + -4.5 x = -8.077747211 + -4.5 Combine like terms: -8.077747211 + -4.5 = -12.577747211 x = -12.577747211 Simplifying x = -12.577747211Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.577747211, -12.577747211}Solution
x = {3.577747211, -12.577747211}
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