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Simplifying 2(3x2 + -4x + -180) = 0 Reorder the terms: 2(-180 + -4x + 3x2) = 0 (-180 * 2 + -4x * 2 + 3x2 * 2) = 0 (-360 + -8x + 6x2) = 0 Solving -360 + -8x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-180 + -4x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-180 + -4x + 3x2)' equal to zero and attempt to solve: Simplifying -180 + -4x + 3x2 = 0 Solving -180 + -4x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -60 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '60' to each side of the equation. -60 + -1.333333333x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + -1.333333333x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + -1.333333333x + x2 = 0 + 60 -1.333333333x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 -1.333333333x + x2 = 60 The x term is -1.333333333x. Take half its coefficient (-0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. -1.333333333x + 0.4444444442 + x2 = 60 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = 60 + 0.4444444442 Combine like terms: 60 + 0.4444444442 = 60.4444444442 0.4444444442 + -1.333333333x + x2 = 60.4444444442 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = 60.4444444442 Calculate the square root of the right side: 7.774602526 Break this problem into two subproblems by setting (x + -0.6666666665) equal to 7.774602526 and -7.774602526.Subproblem 1
x + -0.6666666665 = 7.774602526 Simplifying x + -0.6666666665 = 7.774602526 Reorder the terms: -0.6666666665 + x = 7.774602526 Solving -0.6666666665 + x = 7.774602526 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = 7.774602526 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = 7.774602526 + 0.6666666665 x = 7.774602526 + 0.6666666665 Combine like terms: 7.774602526 + 0.6666666665 = 8.4412691925 x = 8.4412691925 Simplifying x = 8.4412691925Subproblem 2
x + -0.6666666665 = -7.774602526 Simplifying x + -0.6666666665 = -7.774602526 Reorder the terms: -0.6666666665 + x = -7.774602526 Solving -0.6666666665 + x = -7.774602526 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = -7.774602526 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = -7.774602526 + 0.6666666665 x = -7.774602526 + 0.6666666665 Combine like terms: -7.774602526 + 0.6666666665 = -7.1079358595 x = -7.1079358595 Simplifying x = -7.1079358595Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.4412691925, -7.1079358595}Solution
x = {8.4412691925, -7.1079358595}
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