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Simplifying (3x2 + 5x + -12) + -1(x2 + 4x + 9) = x2 + 13x + 6 Reorder the terms: (-12 + 5x + 3x2) + -1(x2 + 4x + 9) = x2 + 13x + 6 Remove parenthesis around (-12 + 5x + 3x2) -12 + 5x + 3x2 + -1(x2 + 4x + 9) = x2 + 13x + 6 Reorder the terms: -12 + 5x + 3x2 + -1(9 + 4x + x2) = x2 + 13x + 6 -12 + 5x + 3x2 + (9 * -1 + 4x * -1 + x2 * -1) = x2 + 13x + 6 -12 + 5x + 3x2 + (-9 + -4x + -1x2) = x2 + 13x + 6 Reorder the terms: -12 + -9 + 5x + -4x + 3x2 + -1x2 = x2 + 13x + 6 Combine like terms: -12 + -9 = -21 -21 + 5x + -4x + 3x2 + -1x2 = x2 + 13x + 6 Combine like terms: 5x + -4x = 1x -21 + 1x + 3x2 + -1x2 = x2 + 13x + 6 Combine like terms: 3x2 + -1x2 = 2x2 -21 + 1x + 2x2 = x2 + 13x + 6 Reorder the terms: -21 + 1x + 2x2 = 6 + 13x + x2 Solving -21 + 1x + 2x2 = 6 + 13x + x2 Solving for variable 'x'. Reorder the terms: -21 + -6 + 1x + -13x + 2x2 + -1x2 = 6 + 13x + x2 + -6 + -13x + -1x2 Combine like terms: -21 + -6 = -27 -27 + 1x + -13x + 2x2 + -1x2 = 6 + 13x + x2 + -6 + -13x + -1x2 Combine like terms: 1x + -13x = -12x -27 + -12x + 2x2 + -1x2 = 6 + 13x + x2 + -6 + -13x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 -27 + -12x + 1x2 = 6 + 13x + x2 + -6 + -13x + -1x2 Reorder the terms: -27 + -12x + 1x2 = 6 + -6 + 13x + -13x + x2 + -1x2 Combine like terms: 6 + -6 = 0 -27 + -12x + 1x2 = 0 + 13x + -13x + x2 + -1x2 -27 + -12x + 1x2 = 13x + -13x + x2 + -1x2 Combine like terms: 13x + -13x = 0 -27 + -12x + 1x2 = 0 + x2 + -1x2 -27 + -12x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -27 + -12x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + -12x + 27 + x2 = 0 + 27 Reorder the terms: -27 + 27 + -12x + x2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -12x + x2 = 0 + 27 -12x + x2 = 0 + 27 Combine like terms: 0 + 27 = 27 -12x + x2 = 27 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 27 + 36 Reorder the terms: 36 + -12x + x2 = 27 + 36 Combine like terms: 27 + 36 = 63 36 + -12x + x2 = 63 Factor a perfect square on the left side: (x + -6)(x + -6) = 63 Calculate the square root of the right side: 7.937253933 Break this problem into two subproblems by setting (x + -6) equal to 7.937253933 and -7.937253933.Subproblem 1
x + -6 = 7.937253933 Simplifying x + -6 = 7.937253933 Reorder the terms: -6 + x = 7.937253933 Solving -6 + x = 7.937253933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 7.937253933 + 6 Combine like terms: -6 + 6 = 0 0 + x = 7.937253933 + 6 x = 7.937253933 + 6 Combine like terms: 7.937253933 + 6 = 13.937253933 x = 13.937253933 Simplifying x = 13.937253933Subproblem 2
x + -6 = -7.937253933 Simplifying x + -6 = -7.937253933 Reorder the terms: -6 + x = -7.937253933 Solving -6 + x = -7.937253933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -7.937253933 + 6 Combine like terms: -6 + 6 = 0 0 + x = -7.937253933 + 6 x = -7.937253933 + 6 Combine like terms: -7.937253933 + 6 = -1.937253933 x = -1.937253933 Simplifying x = -1.937253933Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.937253933, -1.937253933}
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