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Simplifying 6x2 + 18x + -180 = 0 Reorder the terms: -180 + 18x + 6x2 = 0 Solving -180 + 18x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(-30 + 3x + x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-30 + 3x + x2)' equal to zero and attempt to solve: Simplifying -30 + 3x + x2 = 0 Solving -30 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + 3x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + 3x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 3x + x2 = 0 + 30 3x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 3x + x2 = 30 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 30 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 30 + 2.25 Combine like terms: 30 + 2.25 = 32.25 2.25 + 3x + x2 = 32.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 32.25 Calculate the square root of the right side: 5.678908346 Break this problem into two subproblems by setting (x + 1.5) equal to 5.678908346 and -5.678908346.Subproblem 1
x + 1.5 = 5.678908346 Simplifying x + 1.5 = 5.678908346 Reorder the terms: 1.5 + x = 5.678908346 Solving 1.5 + x = 5.678908346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 5.678908346 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 5.678908346 + -1.5 x = 5.678908346 + -1.5 Combine like terms: 5.678908346 + -1.5 = 4.178908346 x = 4.178908346 Simplifying x = 4.178908346Subproblem 2
x + 1.5 = -5.678908346 Simplifying x + 1.5 = -5.678908346 Reorder the terms: 1.5 + x = -5.678908346 Solving 1.5 + x = -5.678908346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -5.678908346 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -5.678908346 + -1.5 x = -5.678908346 + -1.5 Combine like terms: -5.678908346 + -1.5 = -7.178908346 x = -7.178908346 Simplifying x = -7.178908346Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.178908346, -7.178908346}Solution
x = {4.178908346, -7.178908346}
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