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Simplifying 2x + x + (2x + -3) + 2x(x + -1) = 76 Reorder the terms: 2x + x + (-3 + 2x) + 2x(x + -1) = 76 Remove parenthesis around (-3 + 2x) 2x + x + -3 + 2x + 2x(x + -1) = 76 Reorder the terms: 2x + x + -3 + 2x + 2x(-1 + x) = 76 2x + x + -3 + 2x + (-1 * 2x + x * 2x) = 76 2x + x + -3 + 2x + (-2x + 2x2) = 76 Reorder the terms: -3 + 2x + x + 2x + -2x + 2x2 = 76 Combine like terms: 2x + x = 3x -3 + 3x + 2x + -2x + 2x2 = 76 Combine like terms: 3x + 2x = 5x -3 + 5x + -2x + 2x2 = 76 Combine like terms: 5x + -2x = 3x -3 + 3x + 2x2 = 76 Solving -3 + 3x + 2x2 = 76 Solving for variable 'x'. Reorder the terms: -3 + -76 + 3x + 2x2 = 76 + -76 Combine like terms: -3 + -76 = -79 -79 + 3x + 2x2 = 76 + -76 Combine like terms: 76 + -76 = 0 -79 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -39.5 + 1.5x + x2 = 0 Move the constant term to the right: Add '39.5' to each side of the equation. -39.5 + 1.5x + 39.5 + x2 = 0 + 39.5 Reorder the terms: -39.5 + 39.5 + 1.5x + x2 = 0 + 39.5 Combine like terms: -39.5 + 39.5 = 0.0 0.0 + 1.5x + x2 = 0 + 39.5 1.5x + x2 = 0 + 39.5 Combine like terms: 0 + 39.5 = 39.5 1.5x + x2 = 39.5 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 39.5 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 39.5 + 0.5625 Combine like terms: 39.5 + 0.5625 = 40.0625 0.5625 + 1.5x + x2 = 40.0625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 40.0625 Calculate the square root of the right side: 6.329494451 Break this problem into two subproblems by setting (x + 0.75) equal to 6.329494451 and -6.329494451.Subproblem 1
x + 0.75 = 6.329494451 Simplifying x + 0.75 = 6.329494451 Reorder the terms: 0.75 + x = 6.329494451 Solving 0.75 + x = 6.329494451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 6.329494451 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 6.329494451 + -0.75 x = 6.329494451 + -0.75 Combine like terms: 6.329494451 + -0.75 = 5.579494451 x = 5.579494451 Simplifying x = 5.579494451Subproblem 2
x + 0.75 = -6.329494451 Simplifying x + 0.75 = -6.329494451 Reorder the terms: 0.75 + x = -6.329494451 Solving 0.75 + x = -6.329494451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -6.329494451 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -6.329494451 + -0.75 x = -6.329494451 + -0.75 Combine like terms: -6.329494451 + -0.75 = -7.079494451 x = -7.079494451 Simplifying x = -7.079494451Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.579494451, -7.079494451}
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