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Simplifying 9x + 27x2 = 4x + 12 Reorder the terms: 9x + 27x2 = 12 + 4x Solving 9x + 27x2 = 12 + 4x Solving for variable 'x'. Reorder the terms: -12 + 9x + -4x + 27x2 = 12 + 4x + -12 + -4x Combine like terms: 9x + -4x = 5x -12 + 5x + 27x2 = 12 + 4x + -12 + -4x Reorder the terms: -12 + 5x + 27x2 = 12 + -12 + 4x + -4x Combine like terms: 12 + -12 = 0 -12 + 5x + 27x2 = 0 + 4x + -4x -12 + 5x + 27x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -12 + 5x + 27x2 = 0 Begin completing the square. Divide all terms by 27 the coefficient of the squared term: Divide each side by '27'. -0.4444444444 + 0.1851851852x + x2 = 0 Move the constant term to the right: Add '0.4444444444' to each side of the equation. -0.4444444444 + 0.1851851852x + 0.4444444444 + x2 = 0 + 0.4444444444 Reorder the terms: -0.4444444444 + 0.4444444444 + 0.1851851852x + x2 = 0 + 0.4444444444 Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000 0.0000000000 + 0.1851851852x + x2 = 0 + 0.4444444444 0.1851851852x + x2 = 0 + 0.4444444444 Combine like terms: 0 + 0.4444444444 = 0.4444444444 0.1851851852x + x2 = 0.4444444444 The x term is 0.1851851852x. Take half its coefficient (0.0925925926). Square it (0.008573388204) and add it to both sides. Add '0.008573388204' to each side of the equation. 0.1851851852x + 0.008573388204 + x2 = 0.4444444444 + 0.008573388204 Reorder the terms: 0.008573388204 + 0.1851851852x + x2 = 0.4444444444 + 0.008573388204 Combine like terms: 0.4444444444 + 0.008573388204 = 0.453017832604 0.008573388204 + 0.1851851852x + x2 = 0.453017832604 Factor a perfect square on the left side: (x + 0.0925925926)(x + 0.0925925926) = 0.453017832604 Calculate the square root of the right side: 0.673065994 Break this problem into two subproblems by setting (x + 0.0925925926) equal to 0.673065994 and -0.673065994.Subproblem 1
x + 0.0925925926 = 0.673065994 Simplifying x + 0.0925925926 = 0.673065994 Reorder the terms: 0.0925925926 + x = 0.673065994 Solving 0.0925925926 + x = 0.673065994 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0925925926' to each side of the equation. 0.0925925926 + -0.0925925926 + x = 0.673065994 + -0.0925925926 Combine like terms: 0.0925925926 + -0.0925925926 = 0.0000000000 0.0000000000 + x = 0.673065994 + -0.0925925926 x = 0.673065994 + -0.0925925926 Combine like terms: 0.673065994 + -0.0925925926 = 0.5804734014 x = 0.5804734014 Simplifying x = 0.5804734014Subproblem 2
x + 0.0925925926 = -0.673065994 Simplifying x + 0.0925925926 = -0.673065994 Reorder the terms: 0.0925925926 + x = -0.673065994 Solving 0.0925925926 + x = -0.673065994 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0925925926' to each side of the equation. 0.0925925926 + -0.0925925926 + x = -0.673065994 + -0.0925925926 Combine like terms: 0.0925925926 + -0.0925925926 = 0.0000000000 0.0000000000 + x = -0.673065994 + -0.0925925926 x = -0.673065994 + -0.0925925926 Combine like terms: -0.673065994 + -0.0925925926 = -0.7656585866 x = -0.7656585866 Simplifying x = -0.7656585866Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5804734014, -0.7656585866}
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