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Simplifying 2x + -14 = 3(x + 3)(x + 3) + -8x2 Reorder the terms: -14 + 2x = 3(x + 3)(x + 3) + -8x2 Reorder the terms: -14 + 2x = 3(3 + x)(x + 3) + -8x2 Reorder the terms: -14 + 2x = 3(3 + x)(3 + x) + -8x2 Multiply (3 + x) * (3 + x) -14 + 2x = 3(3(3 + x) + x(3 + x)) + -8x2 -14 + 2x = 3((3 * 3 + x * 3) + x(3 + x)) + -8x2 -14 + 2x = 3((9 + 3x) + x(3 + x)) + -8x2 -14 + 2x = 3(9 + 3x + (3 * x + x * x)) + -8x2 -14 + 2x = 3(9 + 3x + (3x + x2)) + -8x2 Combine like terms: 3x + 3x = 6x -14 + 2x = 3(9 + 6x + x2) + -8x2 -14 + 2x = (9 * 3 + 6x * 3 + x2 * 3) + -8x2 -14 + 2x = (27 + 18x + 3x2) + -8x2 Combine like terms: 3x2 + -8x2 = -5x2 -14 + 2x = 27 + 18x + -5x2 Solving -14 + 2x = 27 + 18x + -5x2 Solving for variable 'x'. Reorder the terms: -14 + -27 + 2x + -18x + 5x2 = 27 + 18x + -5x2 + -27 + -18x + 5x2 Combine like terms: -14 + -27 = -41 -41 + 2x + -18x + 5x2 = 27 + 18x + -5x2 + -27 + -18x + 5x2 Combine like terms: 2x + -18x = -16x -41 + -16x + 5x2 = 27 + 18x + -5x2 + -27 + -18x + 5x2 Reorder the terms: -41 + -16x + 5x2 = 27 + -27 + 18x + -18x + -5x2 + 5x2 Combine like terms: 27 + -27 = 0 -41 + -16x + 5x2 = 0 + 18x + -18x + -5x2 + 5x2 -41 + -16x + 5x2 = 18x + -18x + -5x2 + 5x2 Combine like terms: 18x + -18x = 0 -41 + -16x + 5x2 = 0 + -5x2 + 5x2 -41 + -16x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 -41 + -16x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -8.2 + -3.2x + x2 = 0 Move the constant term to the right: Add '8.2' to each side of the equation. -8.2 + -3.2x + 8.2 + x2 = 0 + 8.2 Reorder the terms: -8.2 + 8.2 + -3.2x + x2 = 0 + 8.2 Combine like terms: -8.2 + 8.2 = 0.0 0.0 + -3.2x + x2 = 0 + 8.2 -3.2x + x2 = 0 + 8.2 Combine like terms: 0 + 8.2 = 8.2 -3.2x + x2 = 8.2 The x term is -3.2x. Take half its coefficient (-1.6). Square it (2.56) and add it to both sides. Add '2.56' to each side of the equation. -3.2x + 2.56 + x2 = 8.2 + 2.56 Reorder the terms: 2.56 + -3.2x + x2 = 8.2 + 2.56 Combine like terms: 8.2 + 2.56 = 10.76 2.56 + -3.2x + x2 = 10.76 Factor a perfect square on the left side: (x + -1.6)(x + -1.6) = 10.76 Calculate the square root of the right side: 3.280243893 Break this problem into two subproblems by setting (x + -1.6) equal to 3.280243893 and -3.280243893.Subproblem 1
x + -1.6 = 3.280243893 Simplifying x + -1.6 = 3.280243893 Reorder the terms: -1.6 + x = 3.280243893 Solving -1.6 + x = 3.280243893 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + x = 3.280243893 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = 3.280243893 + 1.6 x = 3.280243893 + 1.6 Combine like terms: 3.280243893 + 1.6 = 4.880243893 x = 4.880243893 Simplifying x = 4.880243893Subproblem 2
x + -1.6 = -3.280243893 Simplifying x + -1.6 = -3.280243893 Reorder the terms: -1.6 + x = -3.280243893 Solving -1.6 + x = -3.280243893 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + x = -3.280243893 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = -3.280243893 + 1.6 x = -3.280243893 + 1.6 Combine like terms: -3.280243893 + 1.6 = -1.680243893 x = -1.680243893 Simplifying x = -1.680243893Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.880243893, -1.680243893}
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