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Simplifying (5x + 3)(x + -4) = 2 Reorder the terms: (3 + 5x)(x + -4) = 2 Reorder the terms: (3 + 5x)(-4 + x) = 2 Multiply (3 + 5x) * (-4 + x) (3(-4 + x) + 5x * (-4 + x)) = 2 ((-4 * 3 + x * 3) + 5x * (-4 + x)) = 2 ((-12 + 3x) + 5x * (-4 + x)) = 2 (-12 + 3x + (-4 * 5x + x * 5x)) = 2 (-12 + 3x + (-20x + 5x2)) = 2 Combine like terms: 3x + -20x = -17x (-12 + -17x + 5x2) = 2 Solving -12 + -17x + 5x2 = 2 Solving for variable 'x'. Reorder the terms: -12 + -2 + -17x + 5x2 = 2 + -2 Combine like terms: -12 + -2 = -14 -14 + -17x + 5x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -14 + -17x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.8 + -3.4x + x2 = 0 Move the constant term to the right: Add '2.8' to each side of the equation. -2.8 + -3.4x + 2.8 + x2 = 0 + 2.8 Reorder the terms: -2.8 + 2.8 + -3.4x + x2 = 0 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + -3.4x + x2 = 0 + 2.8 -3.4x + x2 = 0 + 2.8 Combine like terms: 0 + 2.8 = 2.8 -3.4x + x2 = 2.8 The x term is -3.4x. Take half its coefficient (-1.7). Square it (2.89) and add it to both sides. Add '2.89' to each side of the equation. -3.4x + 2.89 + x2 = 2.8 + 2.89 Reorder the terms: 2.89 + -3.4x + x2 = 2.8 + 2.89 Combine like terms: 2.8 + 2.89 = 5.69 2.89 + -3.4x + x2 = 5.69 Factor a perfect square on the left side: (x + -1.7)(x + -1.7) = 5.69 Calculate the square root of the right side: 2.385372088 Break this problem into two subproblems by setting (x + -1.7) equal to 2.385372088 and -2.385372088.Subproblem 1
x + -1.7 = 2.385372088 Simplifying x + -1.7 = 2.385372088 Reorder the terms: -1.7 + x = 2.385372088 Solving -1.7 + x = 2.385372088 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.7' to each side of the equation. -1.7 + 1.7 + x = 2.385372088 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + x = 2.385372088 + 1.7 x = 2.385372088 + 1.7 Combine like terms: 2.385372088 + 1.7 = 4.085372088 x = 4.085372088 Simplifying x = 4.085372088Subproblem 2
x + -1.7 = -2.385372088 Simplifying x + -1.7 = -2.385372088 Reorder the terms: -1.7 + x = -2.385372088 Solving -1.7 + x = -2.385372088 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.7' to each side of the equation. -1.7 + 1.7 + x = -2.385372088 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + x = -2.385372088 + 1.7 x = -2.385372088 + 1.7 Combine like terms: -2.385372088 + 1.7 = -0.685372088 x = -0.685372088 Simplifying x = -0.685372088Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.085372088, -0.685372088}
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