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Simplifying -3(x + 3) + 2(8x + 6)(2x + 2) = 0 Reorder the terms: -3(3 + x) + 2(8x + 6)(2x + 2) = 0 (3 * -3 + x * -3) + 2(8x + 6)(2x + 2) = 0 (-9 + -3x) + 2(8x + 6)(2x + 2) = 0 Reorder the terms: -9 + -3x + 2(6 + 8x)(2x + 2) = 0 Reorder the terms: -9 + -3x + 2(6 + 8x)(2 + 2x) = 0 Multiply (6 + 8x) * (2 + 2x) -9 + -3x + 2(6(2 + 2x) + 8x * (2 + 2x)) = 0 -9 + -3x + 2((2 * 6 + 2x * 6) + 8x * (2 + 2x)) = 0 -9 + -3x + 2((12 + 12x) + 8x * (2 + 2x)) = 0 -9 + -3x + 2(12 + 12x + (2 * 8x + 2x * 8x)) = 0 -9 + -3x + 2(12 + 12x + (16x + 16x2)) = 0 Combine like terms: 12x + 16x = 28x -9 + -3x + 2(12 + 28x + 16x2) = 0 -9 + -3x + (12 * 2 + 28x * 2 + 16x2 * 2) = 0 -9 + -3x + (24 + 56x + 32x2) = 0 Reorder the terms: -9 + 24 + -3x + 56x + 32x2 = 0 Combine like terms: -9 + 24 = 15 15 + -3x + 56x + 32x2 = 0 Combine like terms: -3x + 56x = 53x 15 + 53x + 32x2 = 0 Solving 15 + 53x + 32x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. 0.46875 + 1.65625x + x2 = 0 Move the constant term to the right: Add '-0.46875' to each side of the equation. 0.46875 + 1.65625x + -0.46875 + x2 = 0 + -0.46875 Reorder the terms: 0.46875 + -0.46875 + 1.65625x + x2 = 0 + -0.46875 Combine like terms: 0.46875 + -0.46875 = 0.00000 0.00000 + 1.65625x + x2 = 0 + -0.46875 1.65625x + x2 = 0 + -0.46875 Combine like terms: 0 + -0.46875 = -0.46875 1.65625x + x2 = -0.46875 The x term is 1.65625x. Take half its coefficient (0.828125). Square it (0.6857910156) and add it to both sides. Add '0.6857910156' to each side of the equation. 1.65625x + 0.6857910156 + x2 = -0.46875 + 0.6857910156 Reorder the terms: 0.6857910156 + 1.65625x + x2 = -0.46875 + 0.6857910156 Combine like terms: -0.46875 + 0.6857910156 = 0.2170410156 0.6857910156 + 1.65625x + x2 = 0.2170410156 Factor a perfect square on the left side: (x + 0.828125)(x + 0.828125) = 0.2170410156 Calculate the square root of the right side: 0.46587661 Break this problem into two subproblems by setting (x + 0.828125) equal to 0.46587661 and -0.46587661.Subproblem 1
x + 0.828125 = 0.46587661 Simplifying x + 0.828125 = 0.46587661 Reorder the terms: 0.828125 + x = 0.46587661 Solving 0.828125 + x = 0.46587661 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.828125' to each side of the equation. 0.828125 + -0.828125 + x = 0.46587661 + -0.828125 Combine like terms: 0.828125 + -0.828125 = 0.000000 0.000000 + x = 0.46587661 + -0.828125 x = 0.46587661 + -0.828125 Combine like terms: 0.46587661 + -0.828125 = -0.36224839 x = -0.36224839 Simplifying x = -0.36224839Subproblem 2
x + 0.828125 = -0.46587661 Simplifying x + 0.828125 = -0.46587661 Reorder the terms: 0.828125 + x = -0.46587661 Solving 0.828125 + x = -0.46587661 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.828125' to each side of the equation. 0.828125 + -0.828125 + x = -0.46587661 + -0.828125 Combine like terms: 0.828125 + -0.828125 = 0.000000 0.000000 + x = -0.46587661 + -0.828125 x = -0.46587661 + -0.828125 Combine like terms: -0.46587661 + -0.828125 = -1.29400161 x = -1.29400161 Simplifying x = -1.29400161Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.36224839, -1.29400161}
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