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Simplifying 30X2 + -180X = 90 Reorder the terms: -180X + 30X2 = 90 Solving -180X + 30X2 = 90 Solving for variable 'X'. Reorder the terms: -90 + -180X + 30X2 = 90 + -90 Combine like terms: 90 + -90 = 0 -90 + -180X + 30X2 = 0 Factor out the Greatest Common Factor (GCF), '30'. 30(-3 + -6X + X2) = 0 Ignore the factor 30.Subproblem 1
Set the factor '(-3 + -6X + X2)' equal to zero and attempt to solve: Simplifying -3 + -6X + X2 = 0 Solving -3 + -6X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -6X + 3 + X2 = 0 + 3 Reorder the terms: -3 + 3 + -6X + X2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -6X + X2 = 0 + 3 -6X + X2 = 0 + 3 Combine like terms: 0 + 3 = 3 -6X + X2 = 3 The X term is -6X. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6X + 9 + X2 = 3 + 9 Reorder the terms: 9 + -6X + X2 = 3 + 9 Combine like terms: 3 + 9 = 12 9 + -6X + X2 = 12 Factor a perfect square on the left side: (X + -3)(X + -3) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (X + -3) equal to 3.464101615 and -3.464101615.Subproblem 1
X + -3 = 3.464101615 Simplifying X + -3 = 3.464101615 Reorder the terms: -3 + X = 3.464101615 Solving -3 + X = 3.464101615 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + X = 3.464101615 + 3 Combine like terms: -3 + 3 = 0 0 + X = 3.464101615 + 3 X = 3.464101615 + 3 Combine like terms: 3.464101615 + 3 = 6.464101615 X = 6.464101615 Simplifying X = 6.464101615Subproblem 2
X + -3 = -3.464101615 Simplifying X + -3 = -3.464101615 Reorder the terms: -3 + X = -3.464101615 Solving -3 + X = -3.464101615 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + X = -3.464101615 + 3 Combine like terms: -3 + 3 = 0 0 + X = -3.464101615 + 3 X = -3.464101615 + 3 Combine like terms: -3.464101615 + 3 = -0.464101615 X = -0.464101615 Simplifying X = -0.464101615Solution
The solution to the problem is based on the solutions from the subproblems. X = {6.464101615, -0.464101615}Solution
X = {6.464101615, -0.464101615}
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