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Simplifying 8x(x + 3) + 2 = 3x(x + 5) Reorder the terms: 8x(3 + x) + 2 = 3x(x + 5) (3 * 8x + x * 8x) + 2 = 3x(x + 5) (24x + 8x2) + 2 = 3x(x + 5) Reorder the terms: 2 + 24x + 8x2 = 3x(x + 5) Reorder the terms: 2 + 24x + 8x2 = 3x(5 + x) 2 + 24x + 8x2 = (5 * 3x + x * 3x) 2 + 24x + 8x2 = (15x + 3x2) Solving 2 + 24x + 8x2 = 15x + 3x2 Solving for variable 'x'. Reorder the terms: 2 + 24x + -15x + 8x2 + -3x2 = 15x + 3x2 + -15x + -3x2 Combine like terms: 24x + -15x = 9x 2 + 9x + 8x2 + -3x2 = 15x + 3x2 + -15x + -3x2 Combine like terms: 8x2 + -3x2 = 5x2 2 + 9x + 5x2 = 15x + 3x2 + -15x + -3x2 Reorder the terms: 2 + 9x + 5x2 = 15x + -15x + 3x2 + -3x2 Combine like terms: 15x + -15x = 0 2 + 9x + 5x2 = 0 + 3x2 + -3x2 2 + 9x + 5x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 2 + 9x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.4 + 1.8x + x2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + 1.8x + -0.4 + x2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + 1.8x + x2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + 1.8x + x2 = 0 + -0.4 1.8x + x2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 1.8x + x2 = -0.4 The x term is 1.8x. Take half its coefficient (0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. 1.8x + 0.81 + x2 = -0.4 + 0.81 Reorder the terms: 0.81 + 1.8x + x2 = -0.4 + 0.81 Combine like terms: -0.4 + 0.81 = 0.41 0.81 + 1.8x + x2 = 0.41 Factor a perfect square on the left side: (x + 0.9)(x + 0.9) = 0.41 Calculate the square root of the right side: 0.640312424 Break this problem into two subproblems by setting (x + 0.9) equal to 0.640312424 and -0.640312424.Subproblem 1
x + 0.9 = 0.640312424 Simplifying x + 0.9 = 0.640312424 Reorder the terms: 0.9 + x = 0.640312424 Solving 0.9 + x = 0.640312424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x = 0.640312424 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = 0.640312424 + -0.9 x = 0.640312424 + -0.9 Combine like terms: 0.640312424 + -0.9 = -0.259687576 x = -0.259687576 Simplifying x = -0.259687576Subproblem 2
x + 0.9 = -0.640312424 Simplifying x + 0.9 = -0.640312424 Reorder the terms: 0.9 + x = -0.640312424 Solving 0.9 + x = -0.640312424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x = -0.640312424 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = -0.640312424 + -0.9 x = -0.640312424 + -0.9 Combine like terms: -0.640312424 + -0.9 = -1.540312424 x = -1.540312424 Simplifying x = -1.540312424Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.259687576, -1.540312424}
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