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Simplifying (4x + -2)(5x + -3) + -25x + 9 = 0 Reorder the terms: (-2 + 4x)(5x + -3) + -25x + 9 = 0 Reorder the terms: (-2 + 4x)(-3 + 5x) + -25x + 9 = 0 Multiply (-2 + 4x) * (-3 + 5x) (-2(-3 + 5x) + 4x * (-3 + 5x)) + -25x + 9 = 0 ((-3 * -2 + 5x * -2) + 4x * (-3 + 5x)) + -25x + 9 = 0 ((6 + -10x) + 4x * (-3 + 5x)) + -25x + 9 = 0 (6 + -10x + (-3 * 4x + 5x * 4x)) + -25x + 9 = 0 (6 + -10x + (-12x + 20x2)) + -25x + 9 = 0 Combine like terms: -10x + -12x = -22x (6 + -22x + 20x2) + -25x + 9 = 0 Reorder the terms: 6 + 9 + -22x + -25x + 20x2 = 0 Combine like terms: 6 + 9 = 15 15 + -22x + -25x + 20x2 = 0 Combine like terms: -22x + -25x = -47x 15 + -47x + 20x2 = 0 Solving 15 + -47x + 20x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. 0.75 + -2.35x + x2 = 0.0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + -2.35x + -0.75 + x2 = 0.0 + -0.75 Reorder the terms: 0.75 + -0.75 + -2.35x + x2 = 0.0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + -2.35x + x2 = 0.0 + -0.75 -2.35x + x2 = 0.0 + -0.75 Combine like terms: 0.0 + -0.75 = -0.75 -2.35x + x2 = -0.75 The x term is -2.35x. Take half its coefficient (-1.175). Square it (1.380625) and add it to both sides. Add '1.380625' to each side of the equation. -2.35x + 1.380625 + x2 = -0.75 + 1.380625 Reorder the terms: 1.380625 + -2.35x + x2 = -0.75 + 1.380625 Combine like terms: -0.75 + 1.380625 = 0.630625 1.380625 + -2.35x + x2 = 0.630625 Factor a perfect square on the left side: (x + -1.175)(x + -1.175) = 0.630625 Calculate the square root of the right side: 0.794119009 Break this problem into two subproblems by setting (x + -1.175) equal to 0.794119009 and -0.794119009.Subproblem 1
x + -1.175 = 0.794119009 Simplifying x + -1.175 = 0.794119009 Reorder the terms: -1.175 + x = 0.794119009 Solving -1.175 + x = 0.794119009 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.175' to each side of the equation. -1.175 + 1.175 + x = 0.794119009 + 1.175 Combine like terms: -1.175 + 1.175 = 0.000 0.000 + x = 0.794119009 + 1.175 x = 0.794119009 + 1.175 Combine like terms: 0.794119009 + 1.175 = 1.969119009 x = 1.969119009 Simplifying x = 1.969119009Subproblem 2
x + -1.175 = -0.794119009 Simplifying x + -1.175 = -0.794119009 Reorder the terms: -1.175 + x = -0.794119009 Solving -1.175 + x = -0.794119009 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.175' to each side of the equation. -1.175 + 1.175 + x = -0.794119009 + 1.175 Combine like terms: -1.175 + 1.175 = 0.000 0.000 + x = -0.794119009 + 1.175 x = -0.794119009 + 1.175 Combine like terms: -0.794119009 + 1.175 = 0.380880991 x = 0.380880991 Simplifying x = 0.380880991Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.969119009, 0.380880991}
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