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Simplifying 30x2 + -81x + -66 = 0 Reorder the terms: -66 + -81x + 30x2 = 0 Solving -66 + -81x + 30x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-22 + -27x + 10x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-22 + -27x + 10x2)' equal to zero and attempt to solve: Simplifying -22 + -27x + 10x2 = 0 Solving -22 + -27x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -2.2 + -2.7x + x2 = 0.0 Move the constant term to the right: Add '2.2' to each side of the equation. -2.2 + -2.7x + 2.2 + x2 = 0.0 + 2.2 Reorder the terms: -2.2 + 2.2 + -2.7x + x2 = 0.0 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + -2.7x + x2 = 0.0 + 2.2 -2.7x + x2 = 0.0 + 2.2 Combine like terms: 0.0 + 2.2 = 2.2 -2.7x + x2 = 2.2 The x term is -2.7x. Take half its coefficient (-1.35). Square it (1.8225) and add it to both sides. Add '1.8225' to each side of the equation. -2.7x + 1.8225 + x2 = 2.2 + 1.8225 Reorder the terms: 1.8225 + -2.7x + x2 = 2.2 + 1.8225 Combine like terms: 2.2 + 1.8225 = 4.0225 1.8225 + -2.7x + x2 = 4.0225 Factor a perfect square on the left side: (x + -1.35)(x + -1.35) = 4.0225 Calculate the square root of the right side: 2.005617112 Break this problem into two subproblems by setting (x + -1.35) equal to 2.005617112 and -2.005617112.Subproblem 1
x + -1.35 = 2.005617112 Simplifying x + -1.35 = 2.005617112 Reorder the terms: -1.35 + x = 2.005617112 Solving -1.35 + x = 2.005617112 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.35' to each side of the equation. -1.35 + 1.35 + x = 2.005617112 + 1.35 Combine like terms: -1.35 + 1.35 = 0.00 0.00 + x = 2.005617112 + 1.35 x = 2.005617112 + 1.35 Combine like terms: 2.005617112 + 1.35 = 3.355617112 x = 3.355617112 Simplifying x = 3.355617112Subproblem 2
x + -1.35 = -2.005617112 Simplifying x + -1.35 = -2.005617112 Reorder the terms: -1.35 + x = -2.005617112 Solving -1.35 + x = -2.005617112 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.35' to each side of the equation. -1.35 + 1.35 + x = -2.005617112 + 1.35 Combine like terms: -1.35 + 1.35 = 0.00 0.00 + x = -2.005617112 + 1.35 x = -2.005617112 + 1.35 Combine like terms: -2.005617112 + 1.35 = -0.655617112 x = -0.655617112 Simplifying x = -0.655617112Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.355617112, -0.655617112}Solution
x = {3.355617112, -0.655617112}
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