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Simplifying 81x2 = 6x + 9 Reorder the terms: 81x2 = 9 + 6x Solving 81x2 = 9 + 6x Solving for variable 'x'. Reorder the terms: -9 + -6x + 81x2 = 9 + 6x + -9 + -6x Reorder the terms: -9 + -6x + 81x2 = 9 + -9 + 6x + -6x Combine like terms: 9 + -9 = 0 -9 + -6x + 81x2 = 0 + 6x + -6x -9 + -6x + 81x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -9 + -6x + 81x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-3 + -2x + 27x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-3 + -2x + 27x2)' equal to zero and attempt to solve: Simplifying -3 + -2x + 27x2 = 0 Solving -3 + -2x + 27x2 = 0 Begin completing the square. Divide all terms by 27 the coefficient of the squared term: Divide each side by '27'. -0.1111111111 + -0.07407407407x + x2 = 0 Move the constant term to the right: Add '0.1111111111' to each side of the equation. -0.1111111111 + -0.07407407407x + 0.1111111111 + x2 = 0 + 0.1111111111 Reorder the terms: -0.1111111111 + 0.1111111111 + -0.07407407407x + x2 = 0 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + -0.07407407407x + x2 = 0 + 0.1111111111 -0.07407407407x + x2 = 0 + 0.1111111111 Combine like terms: 0 + 0.1111111111 = 0.1111111111 -0.07407407407x + x2 = 0.1111111111 The x term is -0.07407407407x. Take half its coefficient (-0.03703703704). Square it (0.001371742113) and add it to both sides. Add '0.001371742113' to each side of the equation. -0.07407407407x + 0.001371742113 + x2 = 0.1111111111 + 0.001371742113 Reorder the terms: 0.001371742113 + -0.07407407407x + x2 = 0.1111111111 + 0.001371742113 Combine like terms: 0.1111111111 + 0.001371742113 = 0.112482853213 0.001371742113 + -0.07407407407x + x2 = 0.112482853213 Factor a perfect square on the left side: (x + -0.03703703704)(x + -0.03703703704) = 0.112482853213 Calculate the square root of the right side: 0.335384635 Break this problem into two subproblems by setting (x + -0.03703703704) equal to 0.335384635 and -0.335384635.Subproblem 1
x + -0.03703703704 = 0.335384635 Simplifying x + -0.03703703704 = 0.335384635 Reorder the terms: -0.03703703704 + x = 0.335384635 Solving -0.03703703704 + x = 0.335384635 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03703703704' to each side of the equation. -0.03703703704 + 0.03703703704 + x = 0.335384635 + 0.03703703704 Combine like terms: -0.03703703704 + 0.03703703704 = 0.00000000000 0.00000000000 + x = 0.335384635 + 0.03703703704 x = 0.335384635 + 0.03703703704 Combine like terms: 0.335384635 + 0.03703703704 = 0.37242167204 x = 0.37242167204 Simplifying x = 0.37242167204Subproblem 2
x + -0.03703703704 = -0.335384635 Simplifying x + -0.03703703704 = -0.335384635 Reorder the terms: -0.03703703704 + x = -0.335384635 Solving -0.03703703704 + x = -0.335384635 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03703703704' to each side of the equation. -0.03703703704 + 0.03703703704 + x = -0.335384635 + 0.03703703704 Combine like terms: -0.03703703704 + 0.03703703704 = 0.00000000000 0.00000000000 + x = -0.335384635 + 0.03703703704 x = -0.335384635 + 0.03703703704 Combine like terms: -0.335384635 + 0.03703703704 = -0.29834759796 x = -0.29834759796 Simplifying x = -0.29834759796Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.37242167204, -0.29834759796}Solution
x = {0.37242167204, -0.29834759796}
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