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Simplifying 3x(2x + -1) + 4 = 5(5 + 2x) + -8 Reorder the terms: 3x(-1 + 2x) + 4 = 5(5 + 2x) + -8 (-1 * 3x + 2x * 3x) + 4 = 5(5 + 2x) + -8 (-3x + 6x2) + 4 = 5(5 + 2x) + -8 Reorder the terms: 4 + -3x + 6x2 = 5(5 + 2x) + -8 4 + -3x + 6x2 = (5 * 5 + 2x * 5) + -8 4 + -3x + 6x2 = (25 + 10x) + -8 Reorder the terms: 4 + -3x + 6x2 = 25 + -8 + 10x Combine like terms: 25 + -8 = 17 4 + -3x + 6x2 = 17 + 10x Solving 4 + -3x + 6x2 = 17 + 10x Solving for variable 'x'. Reorder the terms: 4 + -17 + -3x + -10x + 6x2 = 17 + 10x + -17 + -10x Combine like terms: 4 + -17 = -13 -13 + -3x + -10x + 6x2 = 17 + 10x + -17 + -10x Combine like terms: -3x + -10x = -13x -13 + -13x + 6x2 = 17 + 10x + -17 + -10x Reorder the terms: -13 + -13x + 6x2 = 17 + -17 + 10x + -10x Combine like terms: 17 + -17 = 0 -13 + -13x + 6x2 = 0 + 10x + -10x -13 + -13x + 6x2 = 10x + -10x Combine like terms: 10x + -10x = 0 -13 + -13x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -2.166666667 + -2.166666667x + x2 = 0 Move the constant term to the right: Add '2.166666667' to each side of the equation. -2.166666667 + -2.166666667x + 2.166666667 + x2 = 0 + 2.166666667 Reorder the terms: -2.166666667 + 2.166666667 + -2.166666667x + x2 = 0 + 2.166666667 Combine like terms: -2.166666667 + 2.166666667 = 0.000000000 0.000000000 + -2.166666667x + x2 = 0 + 2.166666667 -2.166666667x + x2 = 0 + 2.166666667 Combine like terms: 0 + 2.166666667 = 2.166666667 -2.166666667x + x2 = 2.166666667 The x term is -2.166666667x. Take half its coefficient (-1.083333334). Square it (1.173611113) and add it to both sides. Add '1.173611113' to each side of the equation. -2.166666667x + 1.173611113 + x2 = 2.166666667 + 1.173611113 Reorder the terms: 1.173611113 + -2.166666667x + x2 = 2.166666667 + 1.173611113 Combine like terms: 2.166666667 + 1.173611113 = 3.34027778 1.173611113 + -2.166666667x + x2 = 3.34027778 Factor a perfect square on the left side: (x + -1.083333334)(x + -1.083333334) = 3.34027778 Calculate the square root of the right side: 1.827642684 Break this problem into two subproblems by setting (x + -1.083333334) equal to 1.827642684 and -1.827642684.Subproblem 1
x + -1.083333334 = 1.827642684 Simplifying x + -1.083333334 = 1.827642684 Reorder the terms: -1.083333334 + x = 1.827642684 Solving -1.083333334 + x = 1.827642684 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.083333334' to each side of the equation. -1.083333334 + 1.083333334 + x = 1.827642684 + 1.083333334 Combine like terms: -1.083333334 + 1.083333334 = 0.000000000 0.000000000 + x = 1.827642684 + 1.083333334 x = 1.827642684 + 1.083333334 Combine like terms: 1.827642684 + 1.083333334 = 2.910976018 x = 2.910976018 Simplifying x = 2.910976018Subproblem 2
x + -1.083333334 = -1.827642684 Simplifying x + -1.083333334 = -1.827642684 Reorder the terms: -1.083333334 + x = -1.827642684 Solving -1.083333334 + x = -1.827642684 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.083333334' to each side of the equation. -1.083333334 + 1.083333334 + x = -1.827642684 + 1.083333334 Combine like terms: -1.083333334 + 1.083333334 = 0.000000000 0.000000000 + x = -1.827642684 + 1.083333334 x = -1.827642684 + 1.083333334 Combine like terms: -1.827642684 + 1.083333334 = -0.74430935 x = -0.74430935 Simplifying x = -0.74430935Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.910976018, -0.74430935}
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