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Simplifying (2x)(3x + 2) = x + 292 Remove parenthesis around (2x) 2x(3x + 2) = x + 292 Reorder the terms: 2x(2 + 3x) = x + 292 (2 * 2x + 3x * 2x) = x + 292 (4x + 6x2) = x + 292 Reorder the terms: 4x + 6x2 = 292 + x Solving 4x + 6x2 = 292 + x Solving for variable 'x'. Reorder the terms: -292 + 4x + -1x + 6x2 = 292 + x + -292 + -1x Combine like terms: 4x + -1x = 3x -292 + 3x + 6x2 = 292 + x + -292 + -1x Reorder the terms: -292 + 3x + 6x2 = 292 + -292 + x + -1x Combine like terms: 292 + -292 = 0 -292 + 3x + 6x2 = 0 + x + -1x -292 + 3x + 6x2 = x + -1x Combine like terms: x + -1x = 0 -292 + 3x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -48.66666667 + 0.5x + x2 = 0 Move the constant term to the right: Add '48.66666667' to each side of the equation. -48.66666667 + 0.5x + 48.66666667 + x2 = 0 + 48.66666667 Reorder the terms: -48.66666667 + 48.66666667 + 0.5x + x2 = 0 + 48.66666667 Combine like terms: -48.66666667 + 48.66666667 = 0.00000000 0.00000000 + 0.5x + x2 = 0 + 48.66666667 0.5x + x2 = 0 + 48.66666667 Combine like terms: 0 + 48.66666667 = 48.66666667 0.5x + x2 = 48.66666667 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 48.66666667 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 48.66666667 + 0.0625 Combine like terms: 48.66666667 + 0.0625 = 48.72916667 0.0625 + 0.5x + x2 = 48.72916667 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 48.72916667 Calculate the square root of the right side: 6.980627957 Break this problem into two subproblems by setting (x + 0.25) equal to 6.980627957 and -6.980627957.Subproblem 1
x + 0.25 = 6.980627957 Simplifying x + 0.25 = 6.980627957 Reorder the terms: 0.25 + x = 6.980627957 Solving 0.25 + x = 6.980627957 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 6.980627957 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 6.980627957 + -0.25 x = 6.980627957 + -0.25 Combine like terms: 6.980627957 + -0.25 = 6.730627957 x = 6.730627957 Simplifying x = 6.730627957Subproblem 2
x + 0.25 = -6.980627957 Simplifying x + 0.25 = -6.980627957 Reorder the terms: 0.25 + x = -6.980627957 Solving 0.25 + x = -6.980627957 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -6.980627957 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -6.980627957 + -0.25 x = -6.980627957 + -0.25 Combine like terms: -6.980627957 + -0.25 = -7.230627957 x = -7.230627957 Simplifying x = -7.230627957Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.730627957, -7.230627957}
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