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Simplifying 2 + 3(12 + -1x) = 2(x + -6) * 8(x + 1) + 1 2 + (12 * 3 + -1x * 3) = 2(x + -6) * 8(x + 1) + 1 2 + (36 + -3x) = 2(x + -6) * 8(x + 1) + 1 Combine like terms: 2 + 36 = 38 38 + -3x = 2(x + -6) * 8(x + 1) + 1 Reorder the terms: 38 + -3x = 2(-6 + x) * 8(x + 1) + 1 Reorder the terms: 38 + -3x = 2(-6 + x) * 8(1 + x) + 1 Reorder the terms for easier multiplication: 38 + -3x = 2 * 8(-6 + x)(1 + x) + 1 Multiply 2 * 8 38 + -3x = 16(-6 + x)(1 + x) + 1 Multiply (-6 + x) * (1 + x) 38 + -3x = 16(-6(1 + x) + x(1 + x)) + 1 38 + -3x = 16((1 * -6 + x * -6) + x(1 + x)) + 1 38 + -3x = 16((-6 + -6x) + x(1 + x)) + 1 38 + -3x = 16(-6 + -6x + (1 * x + x * x)) + 1 38 + -3x = 16(-6 + -6x + (1x + x2)) + 1 Combine like terms: -6x + 1x = -5x 38 + -3x = 16(-6 + -5x + x2) + 1 38 + -3x = (-6 * 16 + -5x * 16 + x2 * 16) + 1 38 + -3x = (-96 + -80x + 16x2) + 1 Reorder the terms: 38 + -3x = -96 + 1 + -80x + 16x2 Combine like terms: -96 + 1 = -95 38 + -3x = -95 + -80x + 16x2 Solving 38 + -3x = -95 + -80x + 16x2 Solving for variable 'x'. Reorder the terms: 38 + 95 + -3x + 80x + -16x2 = -95 + -80x + 16x2 + 95 + 80x + -16x2 Combine like terms: 38 + 95 = 133 133 + -3x + 80x + -16x2 = -95 + -80x + 16x2 + 95 + 80x + -16x2 Combine like terms: -3x + 80x = 77x 133 + 77x + -16x2 = -95 + -80x + 16x2 + 95 + 80x + -16x2 Reorder the terms: 133 + 77x + -16x2 = -95 + 95 + -80x + 80x + 16x2 + -16x2 Combine like terms: -95 + 95 = 0 133 + 77x + -16x2 = 0 + -80x + 80x + 16x2 + -16x2 133 + 77x + -16x2 = -80x + 80x + 16x2 + -16x2 Combine like terms: -80x + 80x = 0 133 + 77x + -16x2 = 0 + 16x2 + -16x2 133 + 77x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 133 + 77x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -8.3125 + -4.8125x + x2 = 0 Move the constant term to the right: Add '8.3125' to each side of the equation. -8.3125 + -4.8125x + 8.3125 + x2 = 0 + 8.3125 Reorder the terms: -8.3125 + 8.3125 + -4.8125x + x2 = 0 + 8.3125 Combine like terms: -8.3125 + 8.3125 = 0.0000 0.0000 + -4.8125x + x2 = 0 + 8.3125 -4.8125x + x2 = 0 + 8.3125 Combine like terms: 0 + 8.3125 = 8.3125 -4.8125x + x2 = 8.3125 The x term is -4.8125x. Take half its coefficient (-2.40625). Square it (5.790039063) and add it to both sides. Add '5.790039063' to each side of the equation. -4.8125x + 5.790039063 + x2 = 8.3125 + 5.790039063 Reorder the terms: 5.790039063 + -4.8125x + x2 = 8.3125 + 5.790039063 Combine like terms: 8.3125 + 5.790039063 = 14.102539063 5.790039063 + -4.8125x + x2 = 14.102539063 Factor a perfect square on the left side: (x + -2.40625)(x + -2.40625) = 14.102539063 Calculate the square root of the right side: 3.755334747 Break this problem into two subproblems by setting (x + -2.40625) equal to 3.755334747 and -3.755334747.Subproblem 1
x + -2.40625 = 3.755334747 Simplifying x + -2.40625 = 3.755334747 Reorder the terms: -2.40625 + x = 3.755334747 Solving -2.40625 + x = 3.755334747 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.40625' to each side of the equation. -2.40625 + 2.40625 + x = 3.755334747 + 2.40625 Combine like terms: -2.40625 + 2.40625 = 0.00000 0.00000 + x = 3.755334747 + 2.40625 x = 3.755334747 + 2.40625 Combine like terms: 3.755334747 + 2.40625 = 6.161584747 x = 6.161584747 Simplifying x = 6.161584747Subproblem 2
x + -2.40625 = -3.755334747 Simplifying x + -2.40625 = -3.755334747 Reorder the terms: -2.40625 + x = -3.755334747 Solving -2.40625 + x = -3.755334747 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.40625' to each side of the equation. -2.40625 + 2.40625 + x = -3.755334747 + 2.40625 Combine like terms: -2.40625 + 2.40625 = 0.00000 0.00000 + x = -3.755334747 + 2.40625 x = -3.755334747 + 2.40625 Combine like terms: -3.755334747 + 2.40625 = -1.349084747 x = -1.349084747 Simplifying x = -1.349084747Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.161584747, -1.349084747}
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