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Simplifying (9x)(9x) + 6x + -8 = 0 Remove parenthesis around (9x) 9x(9x) + 6x + -8 = 0 Remove parenthesis around (9x) 9x * 9x + 6x + -8 = 0 Reorder the terms for easier multiplication: 9 * 9x * x + 6x + -8 = 0 Multiply 9 * 9 81x * x + 6x + -8 = 0 Multiply x * x 81x2 + 6x + -8 = 0 Reorder the terms: -8 + 6x + 81x2 = 0 Solving -8 + 6x + 81x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 81 the coefficient of the squared term: Divide each side by '81'. -0.0987654321 + 0.07407407407x + x2 = 0 Move the constant term to the right: Add '0.0987654321' to each side of the equation. -0.0987654321 + 0.07407407407x + 0.0987654321 + x2 = 0 + 0.0987654321 Reorder the terms: -0.0987654321 + 0.0987654321 + 0.07407407407x + x2 = 0 + 0.0987654321 Combine like terms: -0.0987654321 + 0.0987654321 = 0.0000000000 0.0000000000 + 0.07407407407x + x2 = 0 + 0.0987654321 0.07407407407x + x2 = 0 + 0.0987654321 Combine like terms: 0 + 0.0987654321 = 0.0987654321 0.07407407407x + x2 = 0.0987654321 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 = 0.0987654321 + 0.001371742113 Reorder the terms: 0.001371742113 + 0.07407407407x + x2 = 0.0987654321 + 0.001371742113 Combine like terms: 0.0987654321 + 0.001371742113 = 0.100137174213 0.001371742113 + 0.07407407407x + x2 = 0.100137174213 Factor a perfect square on the left side: (x + 0.03703703704)(x + 0.03703703704) = 0.100137174213 Calculate the square root of the right side: 0.316444583 Break this problem into two subproblems by setting (x + 0.03703703704) equal to 0.316444583 and -0.316444583.Subproblem 1
x + 0.03703703704 = 0.316444583 Simplifying x + 0.03703703704 = 0.316444583 Reorder the terms: 0.03703703704 + x = 0.316444583 Solving 0.03703703704 + x = 0.316444583 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 = 0.316444583 + -0.03703703704 Combine like terms: 0.03703703704 + -0.03703703704 = 0.00000000000 0.00000000000 + x = 0.316444583 + -0.03703703704 x = 0.316444583 + -0.03703703704 Combine like terms: 0.316444583 + -0.03703703704 = 0.27940754596 x = 0.27940754596 Simplifying x = 0.27940754596Subproblem 2
x + 0.03703703704 = -0.316444583 Simplifying x + 0.03703703704 = -0.316444583 Reorder the terms: 0.03703703704 + x = -0.316444583 Solving 0.03703703704 + x = -0.316444583 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 = -0.316444583 + -0.03703703704 Combine like terms: 0.03703703704 + -0.03703703704 = 0.00000000000 0.00000000000 + x = -0.316444583 + -0.03703703704 x = -0.316444583 + -0.03703703704 Combine like terms: -0.316444583 + -0.03703703704 = -0.35348162004 x = -0.35348162004 Simplifying x = -0.35348162004Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.27940754596, -0.35348162004}
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