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Simplifying 180 = 3x2 + 9x + -6 Reorder the terms: 180 = -6 + 9x + 3x2 Solving 180 = -6 + 9x + 3x2 Solving for variable 'x'. Combine like terms: 180 + 6 = 186 186 + -9x + -3x2 = -6 + 9x + 3x2 + 6 + -9x + -3x2 Reorder the terms: 186 + -9x + -3x2 = -6 + 6 + 9x + -9x + 3x2 + -3x2 Combine like terms: -6 + 6 = 0 186 + -9x + -3x2 = 0 + 9x + -9x + 3x2 + -3x2 186 + -9x + -3x2 = 9x + -9x + 3x2 + -3x2 Combine like terms: 9x + -9x = 0 186 + -9x + -3x2 = 0 + 3x2 + -3x2 186 + -9x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 186 + -9x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(62 + -3x + -1x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(62 + -3x + -1x2)' equal to zero and attempt to solve: Simplifying 62 + -3x + -1x2 = 0 Solving 62 + -3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -62 + 3x + x2 = 0 Move the constant term to the right: Add '62' to each side of the equation. -62 + 3x + 62 + x2 = 0 + 62 Reorder the terms: -62 + 62 + 3x + x2 = 0 + 62 Combine like terms: -62 + 62 = 0 0 + 3x + x2 = 0 + 62 3x + x2 = 0 + 62 Combine like terms: 0 + 62 = 62 3x + x2 = 62 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 = 62 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 62 + 2.25 Combine like terms: 62 + 2.25 = 64.25 2.25 + 3x + x2 = 64.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 64.25 Calculate the square root of the right side: 8.015609771 Break this problem into two subproblems by setting (x + 1.5) equal to 8.015609771 and -8.015609771.Subproblem 1
x + 1.5 = 8.015609771 Simplifying x + 1.5 = 8.015609771 Reorder the terms: 1.5 + x = 8.015609771 Solving 1.5 + x = 8.015609771 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 = 8.015609771 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 8.015609771 + -1.5 x = 8.015609771 + -1.5 Combine like terms: 8.015609771 + -1.5 = 6.515609771 x = 6.515609771 Simplifying x = 6.515609771Subproblem 2
x + 1.5 = -8.015609771 Simplifying x + 1.5 = -8.015609771 Reorder the terms: 1.5 + x = -8.015609771 Solving 1.5 + x = -8.015609771 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 = -8.015609771 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -8.015609771 + -1.5 x = -8.015609771 + -1.5 Combine like terms: -8.015609771 + -1.5 = -9.515609771 x = -9.515609771 Simplifying x = -9.515609771Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.515609771, -9.515609771}Solution
x = {6.515609771, -9.515609771}
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