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Simplifying (5x + -1)(2x + -4) = 9x Reorder the terms: (-1 + 5x)(2x + -4) = 9x Reorder the terms: (-1 + 5x)(-4 + 2x) = 9x Multiply (-1 + 5x) * (-4 + 2x) (-1(-4 + 2x) + 5x * (-4 + 2x)) = 9x ((-4 * -1 + 2x * -1) + 5x * (-4 + 2x)) = 9x ((4 + -2x) + 5x * (-4 + 2x)) = 9x (4 + -2x + (-4 * 5x + 2x * 5x)) = 9x (4 + -2x + (-20x + 10x2)) = 9x Combine like terms: -2x + -20x = -22x (4 + -22x + 10x2) = 9x Solving 4 + -22x + 10x2 = 9x Solving for variable 'x'. Reorder the terms: 4 + -22x + -9x + 10x2 = 9x + -9x Combine like terms: -22x + -9x = -31x 4 + -31x + 10x2 = 9x + -9x Combine like terms: 9x + -9x = 0 4 + -31x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.4 + -3.1x + x2 = 0.0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + -3.1x + -0.4 + x2 = 0.0 + -0.4 Reorder the terms: 0.4 + -0.4 + -3.1x + x2 = 0.0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + -3.1x + x2 = 0.0 + -0.4 -3.1x + x2 = 0.0 + -0.4 Combine like terms: 0.0 + -0.4 = -0.4 -3.1x + x2 = -0.4 The x term is -3.1x. Take half its coefficient (-1.55). Square it (2.4025) and add it to both sides. Add '2.4025' to each side of the equation. -3.1x + 2.4025 + x2 = -0.4 + 2.4025 Reorder the terms: 2.4025 + -3.1x + x2 = -0.4 + 2.4025 Combine like terms: -0.4 + 2.4025 = 2.0025 2.4025 + -3.1x + x2 = 2.0025 Factor a perfect square on the left side: (x + -1.55)(x + -1.55) = 2.0025 Calculate the square root of the right side: 1.41509717 Break this problem into two subproblems by setting (x + -1.55) equal to 1.41509717 and -1.41509717.Subproblem 1
x + -1.55 = 1.41509717 Simplifying x + -1.55 = 1.41509717 Reorder the terms: -1.55 + x = 1.41509717 Solving -1.55 + x = 1.41509717 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.55' to each side of the equation. -1.55 + 1.55 + x = 1.41509717 + 1.55 Combine like terms: -1.55 + 1.55 = 0.00 0.00 + x = 1.41509717 + 1.55 x = 1.41509717 + 1.55 Combine like terms: 1.41509717 + 1.55 = 2.96509717 x = 2.96509717 Simplifying x = 2.96509717Subproblem 2
x + -1.55 = -1.41509717 Simplifying x + -1.55 = -1.41509717 Reorder the terms: -1.55 + x = -1.41509717 Solving -1.55 + x = -1.41509717 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.55' to each side of the equation. -1.55 + 1.55 + x = -1.41509717 + 1.55 Combine like terms: -1.55 + 1.55 = 0.00 0.00 + x = -1.41509717 + 1.55 x = -1.41509717 + 1.55 Combine like terms: -1.41509717 + 1.55 = 0.13490283 x = 0.13490283 Simplifying x = 0.13490283Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.96509717, 0.13490283}
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