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Simplifying 6x2 + 3x + -180 = 0 Reorder the terms: -180 + 3x + 6x2 = 0 Solving -180 + 3x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-60 + x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-60 + x + 2x2)' equal to zero and attempt to solve: Simplifying -60 + x + 2x2 = 0 Solving -60 + x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -30 + 0.5x + x2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + 0.5x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + 0.5x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 0.5x + x2 = 0 + 30 0.5x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 0.5x + x2 = 30 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.5x + 0.25 + x2 = 30 + 0.25 Reorder the terms: 0.25 + 0.5x + x2 = 30 + 0.25 Combine like terms: 30 + 0.25 = 30.25 0.25 + 0.5x + x2 = 30.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 30.25 Calculate the square root of the right side: 5.5 Break this problem into two subproblems by setting (x + 0.5) equal to 5.5 and -5.5.Subproblem 1
x + 0.5 = 5.5 Simplifying x + 0.5 = 5.5 Reorder the terms: 0.5 + x = 5.5 Solving 0.5 + x = 5.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 5.5 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 5.5 + -0.5 x = 5.5 + -0.5 Combine like terms: 5.5 + -0.5 = 5 x = 5 Simplifying x = 5Subproblem 2
x + 0.5 = -5.5 Simplifying x + 0.5 = -5.5 Reorder the terms: 0.5 + x = -5.5 Solving 0.5 + x = -5.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -5.5 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -5.5 + -0.5 x = -5.5 + -0.5 Combine like terms: -5.5 + -0.5 = -6 x = -6 Simplifying x = -6Solution
The solution to the problem is based on the solutions from the subproblems. x = {5, -6}Solution
x = {5, -6}
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