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Simplifying 81x2 + 90x = 21 Reorder the terms: 90x + 81x2 = 21 Solving 90x + 81x2 = 21 Solving for variable 'x'. Reorder the terms: -21 + 90x + 81x2 = 21 + -21 Combine like terms: 21 + -21 = 0 -21 + 90x + 81x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-7 + 30x + 27x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-7 + 30x + 27x2)' equal to zero and attempt to solve: Simplifying -7 + 30x + 27x2 = 0 Solving -7 + 30x + 27x2 = 0 Begin completing the square. Divide all terms by 27 the coefficient of the squared term: Divide each side by '27'. -0.2592592593 + 1.111111111x + x2 = 0 Move the constant term to the right: Add '0.2592592593' to each side of the equation. -0.2592592593 + 1.111111111x + 0.2592592593 + x2 = 0 + 0.2592592593 Reorder the terms: -0.2592592593 + 0.2592592593 + 1.111111111x + x2 = 0 + 0.2592592593 Combine like terms: -0.2592592593 + 0.2592592593 = 0.0000000000 0.0000000000 + 1.111111111x + x2 = 0 + 0.2592592593 1.111111111x + x2 = 0 + 0.2592592593 Combine like terms: 0 + 0.2592592593 = 0.2592592593 1.111111111x + x2 = 0.2592592593 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 = 0.2592592593 + 0.3086419752 Reorder the terms: 0.3086419752 + 1.111111111x + x2 = 0.2592592593 + 0.3086419752 Combine like terms: 0.2592592593 + 0.3086419752 = 0.5679012345 0.3086419752 + 1.111111111x + x2 = 0.5679012345 Factor a perfect square on the left side: (x + 0.5555555555)(x + 0.5555555555) = 0.5679012345 Calculate the square root of the right side: 0.75359222 Break this problem into two subproblems by setting (x + 0.5555555555) equal to 0.75359222 and -0.75359222.Subproblem 1
x + 0.5555555555 = 0.75359222 Simplifying x + 0.5555555555 = 0.75359222 Reorder the terms: 0.5555555555 + x = 0.75359222 Solving 0.5555555555 + x = 0.75359222 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 = 0.75359222 + -0.5555555555 Combine like terms: 0.5555555555 + -0.5555555555 = 0.0000000000 0.0000000000 + x = 0.75359222 + -0.5555555555 x = 0.75359222 + -0.5555555555 Combine like terms: 0.75359222 + -0.5555555555 = 0.1980366645 x = 0.1980366645 Simplifying x = 0.1980366645Subproblem 2
x + 0.5555555555 = -0.75359222 Simplifying x + 0.5555555555 = -0.75359222 Reorder the terms: 0.5555555555 + x = -0.75359222 Solving 0.5555555555 + x = -0.75359222 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 = -0.75359222 + -0.5555555555 Combine like terms: 0.5555555555 + -0.5555555555 = 0.0000000000 0.0000000000 + x = -0.75359222 + -0.5555555555 x = -0.75359222 + -0.5555555555 Combine like terms: -0.75359222 + -0.5555555555 = -1.3091477755 x = -1.3091477755 Simplifying x = -1.3091477755Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1980366645, -1.3091477755}Solution
x = {0.1980366645, -1.3091477755}
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