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Simplifying 4x(x + -2) = (2x + -3) Reorder the terms: 4x(-2 + x) = (2x + -3) (-2 * 4x + x * 4x) = (2x + -3) (-8x + 4x2) = (2x + -3) Reorder the terms: -8x + 4x2 = (-3 + 2x) Remove parenthesis around (-3 + 2x) -8x + 4x2 = -3 + 2x Solving -8x + 4x2 = -3 + 2x Solving for variable 'x'. Reorder the terms: 3 + -8x + -2x + 4x2 = -3 + 2x + 3 + -2x Combine like terms: -8x + -2x = -10x 3 + -10x + 4x2 = -3 + 2x + 3 + -2x Reorder the terms: 3 + -10x + 4x2 = -3 + 3 + 2x + -2x Combine like terms: -3 + 3 = 0 3 + -10x + 4x2 = 0 + 2x + -2x 3 + -10x + 4x2 = 2x + -2x Combine like terms: 2x + -2x = 0 3 + -10x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.75 + -2.5x + x2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + -2.5x + -0.75 + x2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + -2.5x + x2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + -2.5x + x2 = 0 + -0.75 -2.5x + x2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 -2.5x + x2 = -0.75 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = -0.75 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = -0.75 + 1.5625 Combine like terms: -0.75 + 1.5625 = 0.8125 1.5625 + -2.5x + x2 = 0.8125 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 0.8125 Calculate the square root of the right side: 0.901387819 Break this problem into two subproblems by setting (x + -1.25) equal to 0.901387819 and -0.901387819.Subproblem 1
x + -1.25 = 0.901387819 Simplifying x + -1.25 = 0.901387819 Reorder the terms: -1.25 + x = 0.901387819 Solving -1.25 + x = 0.901387819 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 0.901387819 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 0.901387819 + 1.25 x = 0.901387819 + 1.25 Combine like terms: 0.901387819 + 1.25 = 2.151387819 x = 2.151387819 Simplifying x = 2.151387819Subproblem 2
x + -1.25 = -0.901387819 Simplifying x + -1.25 = -0.901387819 Reorder the terms: -1.25 + x = -0.901387819 Solving -1.25 + x = -0.901387819 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -0.901387819 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -0.901387819 + 1.25 x = -0.901387819 + 1.25 Combine like terms: -0.901387819 + 1.25 = 0.348612181 x = 0.348612181 Simplifying x = 0.348612181Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.151387819, 0.348612181}
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