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Simplifying (2x + 3)(5x + -1) = 46 Reorder the terms: (3 + 2x)(5x + -1) = 46 Reorder the terms: (3 + 2x)(-1 + 5x) = 46 Multiply (3 + 2x) * (-1 + 5x) (3(-1 + 5x) + 2x * (-1 + 5x)) = 46 ((-1 * 3 + 5x * 3) + 2x * (-1 + 5x)) = 46 ((-3 + 15x) + 2x * (-1 + 5x)) = 46 (-3 + 15x + (-1 * 2x + 5x * 2x)) = 46 (-3 + 15x + (-2x + 10x2)) = 46 Combine like terms: 15x + -2x = 13x (-3 + 13x + 10x2) = 46 Solving -3 + 13x + 10x2 = 46 Solving for variable 'x'. Reorder the terms: -3 + -46 + 13x + 10x2 = 46 + -46 Combine like terms: -3 + -46 = -49 -49 + 13x + 10x2 = 46 + -46 Combine like terms: 46 + -46 = 0 -49 + 13x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -4.9 + 1.3x + x2 = 0.0 Move the constant term to the right: Add '4.9' to each side of the equation. -4.9 + 1.3x + 4.9 + x2 = 0.0 + 4.9 Reorder the terms: -4.9 + 4.9 + 1.3x + x2 = 0.0 + 4.9 Combine like terms: -4.9 + 4.9 = 0.0 0.0 + 1.3x + x2 = 0.0 + 4.9 1.3x + x2 = 0.0 + 4.9 Combine like terms: 0.0 + 4.9 = 4.9 1.3x + x2 = 4.9 The x term is 1.3x. Take half its coefficient (0.65). Square it (0.4225) and add it to both sides. Add '0.4225' to each side of the equation. 1.3x + 0.4225 + x2 = 4.9 + 0.4225 Reorder the terms: 0.4225 + 1.3x + x2 = 4.9 + 0.4225 Combine like terms: 4.9 + 0.4225 = 5.3225 0.4225 + 1.3x + x2 = 5.3225 Factor a perfect square on the left side: (x + 0.65)(x + 0.65) = 5.3225 Calculate the square root of the right side: 2.307054399 Break this problem into two subproblems by setting (x + 0.65) equal to 2.307054399 and -2.307054399.Subproblem 1
x + 0.65 = 2.307054399 Simplifying x + 0.65 = 2.307054399 Reorder the terms: 0.65 + x = 2.307054399 Solving 0.65 + x = 2.307054399 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.65' to each side of the equation. 0.65 + -0.65 + x = 2.307054399 + -0.65 Combine like terms: 0.65 + -0.65 = 0.00 0.00 + x = 2.307054399 + -0.65 x = 2.307054399 + -0.65 Combine like terms: 2.307054399 + -0.65 = 1.657054399 x = 1.657054399 Simplifying x = 1.657054399Subproblem 2
x + 0.65 = -2.307054399 Simplifying x + 0.65 = -2.307054399 Reorder the terms: 0.65 + x = -2.307054399 Solving 0.65 + x = -2.307054399 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.65' to each side of the equation. 0.65 + -0.65 + x = -2.307054399 + -0.65 Combine like terms: 0.65 + -0.65 = 0.00 0.00 + x = -2.307054399 + -0.65 x = -2.307054399 + -0.65 Combine like terms: -2.307054399 + -0.65 = -2.957054399 x = -2.957054399 Simplifying x = -2.957054399Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.657054399, -2.957054399}
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