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Simplifying 81x2 + 90x = 150 Reorder the terms: 90x + 81x2 = 150 Solving 90x + 81x2 = 150 Solving for variable 'x'. Reorder the terms: -150 + 90x + 81x2 = 150 + -150 Combine like terms: 150 + -150 = 0 -150 + 90x + 81x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-50 + 30x + 27x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-50 + 30x + 27x2)' equal to zero and attempt to solve: Simplifying -50 + 30x + 27x2 = 0 Solving -50 + 30x + 27x2 = 0 Begin completing the square. Divide all terms by 27 the coefficient of the squared term: Divide each side by '27'. -1.851851852 + 1.111111111x + x2 = 0 Move the constant term to the right: Add '1.851851852' to each side of the equation. -1.851851852 + 1.111111111x + 1.851851852 + x2 = 0 + 1.851851852 Reorder the terms: -1.851851852 + 1.851851852 + 1.111111111x + x2 = 0 + 1.851851852 Combine like terms: -1.851851852 + 1.851851852 = 0.000000000 0.000000000 + 1.111111111x + x2 = 0 + 1.851851852 1.111111111x + x2 = 0 + 1.851851852 Combine like terms: 0 + 1.851851852 = 1.851851852 1.111111111x + x2 = 1.851851852 The x term is 1.111111111x. Take half its coefficient (0.5555555555). Square it (0.3086419752) and add it to both sides. Add '0.3086419752' to each side of the equation. 1.111111111x + 0.3086419752 + x2 = 1.851851852 + 0.3086419752 Reorder the terms: 0.3086419752 + 1.111111111x + x2 = 1.851851852 + 0.3086419752 Combine like terms: 1.851851852 + 0.3086419752 = 2.1604938272 0.3086419752 + 1.111111111x + x2 = 2.1604938272 Factor a perfect square on the left side: (x + 0.5555555555)(x + 0.5555555555) = 2.1604938272 Calculate the square root of the right side: 1.469861839 Break this problem into two subproblems by setting (x + 0.5555555555) equal to 1.469861839 and -1.469861839.Subproblem 1
x + 0.5555555555 = 1.469861839 Simplifying x + 0.5555555555 = 1.469861839 Reorder the terms: 0.5555555555 + x = 1.469861839 Solving 0.5555555555 + x = 1.469861839 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5555555555' to each side of the equation. 0.5555555555 + -0.5555555555 + x = 1.469861839 + -0.5555555555 Combine like terms: 0.5555555555 + -0.5555555555 = 0.0000000000 0.0000000000 + x = 1.469861839 + -0.5555555555 x = 1.469861839 + -0.5555555555 Combine like terms: 1.469861839 + -0.5555555555 = 0.9143062835 x = 0.9143062835 Simplifying x = 0.9143062835Subproblem 2
x + 0.5555555555 = -1.469861839 Simplifying x + 0.5555555555 = -1.469861839 Reorder the terms: 0.5555555555 + x = -1.469861839 Solving 0.5555555555 + x = -1.469861839 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5555555555' to each side of the equation. 0.5555555555 + -0.5555555555 + x = -1.469861839 + -0.5555555555 Combine like terms: 0.5555555555 + -0.5555555555 = 0.0000000000 0.0000000000 + x = -1.469861839 + -0.5555555555 x = -1.469861839 + -0.5555555555 Combine like terms: -1.469861839 + -0.5555555555 = -2.0254173945 x = -2.0254173945 Simplifying x = -2.0254173945Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9143062835, -2.0254173945}Solution
x = {0.9143062835, -2.0254173945}
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