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Simplifying (6x2 + 4x + -12) + -1(3x2 + 9x + -8) = 0 Reorder the terms: (-12 + 4x + 6x2) + -1(3x2 + 9x + -8) = 0 Remove parenthesis around (-12 + 4x + 6x2) -12 + 4x + 6x2 + -1(3x2 + 9x + -8) = 0 Reorder the terms: -12 + 4x + 6x2 + -1(-8 + 9x + 3x2) = 0 -12 + 4x + 6x2 + (-8 * -1 + 9x * -1 + 3x2 * -1) = 0 -12 + 4x + 6x2 + (8 + -9x + -3x2) = 0 Reorder the terms: -12 + 8 + 4x + -9x + 6x2 + -3x2 = 0 Combine like terms: -12 + 8 = -4 -4 + 4x + -9x + 6x2 + -3x2 = 0 Combine like terms: 4x + -9x = -5x -4 + -5x + 6x2 + -3x2 = 0 Combine like terms: 6x2 + -3x2 = 3x2 -4 + -5x + 3x2 = 0 Solving -4 + -5x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1.333333333 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + -1.666666667x + 1.333333333 + x2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + -1.666666667x + x2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + -1.666666667x + x2 = 0 + 1.333333333 -1.666666667x + x2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 -1.666666667x + x2 = 1.333333333 The x term is -1.666666667x. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667x + 0.6944444447 + x2 = 1.333333333 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = 1.333333333 + 0.6944444447 Combine like terms: 1.333333333 + 0.6944444447 = 2.0277777777 0.6944444447 + -1.666666667x + x2 = 2.0277777777 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = 2.0277777777 Calculate the square root of the right side: 1.424000624 Break this problem into two subproblems by setting (x + -0.8333333335) equal to 1.424000624 and -1.424000624.Subproblem 1
x + -0.8333333335 = 1.424000624 Simplifying x + -0.8333333335 = 1.424000624 Reorder the terms: -0.8333333335 + x = 1.424000624 Solving -0.8333333335 + x = 1.424000624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = 1.424000624 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 1.424000624 + 0.8333333335 x = 1.424000624 + 0.8333333335 Combine like terms: 1.424000624 + 0.8333333335 = 2.2573339575 x = 2.2573339575 Simplifying x = 2.2573339575Subproblem 2
x + -0.8333333335 = -1.424000624 Simplifying x + -0.8333333335 = -1.424000624 Reorder the terms: -0.8333333335 + x = -1.424000624 Solving -0.8333333335 + x = -1.424000624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = -1.424000624 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -1.424000624 + 0.8333333335 x = -1.424000624 + 0.8333333335 Combine like terms: -1.424000624 + 0.8333333335 = -0.5906672905 x = -0.5906672905 Simplifying x = -0.5906672905Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.2573339575, -0.5906672905}
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