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Simplifying 44x2 + -66x + -144 = 0 Reorder the terms: -144 + -66x + 44x2 = 0 Solving -144 + -66x + 44x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-72 + -33x + 22x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-72 + -33x + 22x2)' equal to zero and attempt to solve: Simplifying -72 + -33x + 22x2 = 0 Solving -72 + -33x + 22x2 = 0 Begin completing the square. Divide all terms by 22 the coefficient of the squared term: Divide each side by '22'. -3.272727273 + -1.5x + x2 = 0 Move the constant term to the right: Add '3.272727273' to each side of the equation. -3.272727273 + -1.5x + 3.272727273 + x2 = 0 + 3.272727273 Reorder the terms: -3.272727273 + 3.272727273 + -1.5x + x2 = 0 + 3.272727273 Combine like terms: -3.272727273 + 3.272727273 = 0.000000000 0.000000000 + -1.5x + x2 = 0 + 3.272727273 -1.5x + x2 = 0 + 3.272727273 Combine like terms: 0 + 3.272727273 = 3.272727273 -1.5x + x2 = 3.272727273 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 3.272727273 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 3.272727273 + 0.5625 Combine like terms: 3.272727273 + 0.5625 = 3.835227273 0.5625 + -1.5x + x2 = 3.835227273 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 3.835227273 Calculate the square root of the right side: 1.95837363 Break this problem into two subproblems by setting (x + -0.75) equal to 1.95837363 and -1.95837363.Subproblem 1
x + -0.75 = 1.95837363 Simplifying x + -0.75 = 1.95837363 Reorder the terms: -0.75 + x = 1.95837363 Solving -0.75 + x = 1.95837363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 1.95837363 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 1.95837363 + 0.75 x = 1.95837363 + 0.75 Combine like terms: 1.95837363 + 0.75 = 2.70837363 x = 2.70837363 Simplifying x = 2.70837363Subproblem 2
x + -0.75 = -1.95837363 Simplifying x + -0.75 = -1.95837363 Reorder the terms: -0.75 + x = -1.95837363 Solving -0.75 + x = -1.95837363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -1.95837363 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -1.95837363 + 0.75 x = -1.95837363 + 0.75 Combine like terms: -1.95837363 + 0.75 = -1.20837363 x = -1.20837363 Simplifying x = -1.20837363Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.70837363, -1.20837363}Solution
x = {2.70837363, -1.20837363}
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