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Simplifying 202 = (4x + -1)(5x + 3) Reorder the terms: 202 = (-1 + 4x)(5x + 3) Reorder the terms: 202 = (-1 + 4x)(3 + 5x) Multiply (-1 + 4x) * (3 + 5x) 202 = (-1(3 + 5x) + 4x * (3 + 5x)) 202 = ((3 * -1 + 5x * -1) + 4x * (3 + 5x)) 202 = ((-3 + -5x) + 4x * (3 + 5x)) 202 = (-3 + -5x + (3 * 4x + 5x * 4x)) 202 = (-3 + -5x + (12x + 20x2)) Combine like terms: -5x + 12x = 7x 202 = (-3 + 7x + 20x2) Solving 202 = -3 + 7x + 20x2 Solving for variable 'x'. Combine like terms: 202 + 3 = 205 205 + -7x + -20x2 = -3 + 7x + 20x2 + 3 + -7x + -20x2 Reorder the terms: 205 + -7x + -20x2 = -3 + 3 + 7x + -7x + 20x2 + -20x2 Combine like terms: -3 + 3 = 0 205 + -7x + -20x2 = 0 + 7x + -7x + 20x2 + -20x2 205 + -7x + -20x2 = 7x + -7x + 20x2 + -20x2 Combine like terms: 7x + -7x = 0 205 + -7x + -20x2 = 0 + 20x2 + -20x2 205 + -7x + -20x2 = 20x2 + -20x2 Combine like terms: 20x2 + -20x2 = 0 205 + -7x + -20x2 = 0 Begin completing the square. Divide all terms by -20 the coefficient of the squared term: Divide each side by '-20'. -10.25 + 0.35x + x2 = 0 Move the constant term to the right: Add '10.25' to each side of the equation. -10.25 + 0.35x + 10.25 + x2 = 0 + 10.25 Reorder the terms: -10.25 + 10.25 + 0.35x + x2 = 0 + 10.25 Combine like terms: -10.25 + 10.25 = 0.00 0.00 + 0.35x + x2 = 0 + 10.25 0.35x + x2 = 0 + 10.25 Combine like terms: 0 + 10.25 = 10.25 0.35x + x2 = 10.25 The x term is 0.35x. Take half its coefficient (0.175). Square it (0.030625) and add it to both sides. Add '0.030625' to each side of the equation. 0.35x + 0.030625 + x2 = 10.25 + 0.030625 Reorder the terms: 0.030625 + 0.35x + x2 = 10.25 + 0.030625 Combine like terms: 10.25 + 0.030625 = 10.280625 0.030625 + 0.35x + x2 = 10.280625 Factor a perfect square on the left side: (x + 0.175)(x + 0.175) = 10.280625 Calculate the square root of the right side: 3.206341373 Break this problem into two subproblems by setting (x + 0.175) equal to 3.206341373 and -3.206341373.Subproblem 1
x + 0.175 = 3.206341373 Simplifying x + 0.175 = 3.206341373 Reorder the terms: 0.175 + x = 3.206341373 Solving 0.175 + x = 3.206341373 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.175' to each side of the equation. 0.175 + -0.175 + x = 3.206341373 + -0.175 Combine like terms: 0.175 + -0.175 = 0.000 0.000 + x = 3.206341373 + -0.175 x = 3.206341373 + -0.175 Combine like terms: 3.206341373 + -0.175 = 3.031341373 x = 3.031341373 Simplifying x = 3.031341373Subproblem 2
x + 0.175 = -3.206341373 Simplifying x + 0.175 = -3.206341373 Reorder the terms: 0.175 + x = -3.206341373 Solving 0.175 + x = -3.206341373 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.175' to each side of the equation. 0.175 + -0.175 + x = -3.206341373 + -0.175 Combine like terms: 0.175 + -0.175 = 0.000 0.000 + x = -3.206341373 + -0.175 x = -3.206341373 + -0.175 Combine like terms: -3.206341373 + -0.175 = -3.381341373 x = -3.381341373 Simplifying x = -3.381341373Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.031341373, -3.381341373}
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