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Simplifying 6x2 + 45x = 180 Reorder the terms: 45x + 6x2 = 180 Solving 45x + 6x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + 45x + 6x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + 45x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-60 + 15x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-60 + 15x + 2x2)' equal to zero and attempt to solve: Simplifying -60 + 15x + 2x2 = 0 Solving -60 + 15x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -30 + 7.5x + x2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + 7.5x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + 7.5x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 7.5x + x2 = 0 + 30 7.5x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 7.5x + x2 = 30 The x term is 7.5x. Take half its coefficient (3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. 7.5x + 14.0625 + x2 = 30 + 14.0625 Reorder the terms: 14.0625 + 7.5x + x2 = 30 + 14.0625 Combine like terms: 30 + 14.0625 = 44.0625 14.0625 + 7.5x + x2 = 44.0625 Factor a perfect square on the left side: (x + 3.75)(x + 3.75) = 44.0625 Calculate the square root of the right side: 6.637959024 Break this problem into two subproblems by setting (x + 3.75) equal to 6.637959024 and -6.637959024.Subproblem 1
x + 3.75 = 6.637959024 Simplifying x + 3.75 = 6.637959024 Reorder the terms: 3.75 + x = 6.637959024 Solving 3.75 + x = 6.637959024 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = 6.637959024 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = 6.637959024 + -3.75 x = 6.637959024 + -3.75 Combine like terms: 6.637959024 + -3.75 = 2.887959024 x = 2.887959024 Simplifying x = 2.887959024Subproblem 2
x + 3.75 = -6.637959024 Simplifying x + 3.75 = -6.637959024 Reorder the terms: 3.75 + x = -6.637959024 Solving 3.75 + x = -6.637959024 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = -6.637959024 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = -6.637959024 + -3.75 x = -6.637959024 + -3.75 Combine like terms: -6.637959024 + -3.75 = -10.387959024 x = -10.387959024 Simplifying x = -10.387959024Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.887959024, -10.387959024}Solution
x = {2.887959024, -10.387959024}
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