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Simplifying 4x(5 + -2x) + -3(2 + -1x) = 0 (5 * 4x + -2x * 4x) + -3(2 + -1x) = 0 (20x + -8x2) + -3(2 + -1x) = 0 20x + -8x2 + (2 * -3 + -1x * -3) = 0 20x + -8x2 + (-6 + 3x) = 0 Reorder the terms: -6 + 20x + 3x + -8x2 = 0 Combine like terms: 20x + 3x = 23x -6 + 23x + -8x2 = 0 Solving -6 + 23x + -8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 0.75 + -2.875x + x2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + -2.875x + -0.75 + x2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + -2.875x + x2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + -2.875x + x2 = 0 + -0.75 -2.875x + x2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 -2.875x + x2 = -0.75 The x term is -2.875x. Take half its coefficient (-1.4375). Square it (2.06640625) and add it to both sides. Add '2.06640625' to each side of the equation. -2.875x + 2.06640625 + x2 = -0.75 + 2.06640625 Reorder the terms: 2.06640625 + -2.875x + x2 = -0.75 + 2.06640625 Combine like terms: -0.75 + 2.06640625 = 1.31640625 2.06640625 + -2.875x + x2 = 1.31640625 Factor a perfect square on the left side: (x + -1.4375)(x + -1.4375) = 1.31640625 Calculate the square root of the right side: 1.147347484 Break this problem into two subproblems by setting (x + -1.4375) equal to 1.147347484 and -1.147347484.Subproblem 1
x + -1.4375 = 1.147347484 Simplifying x + -1.4375 = 1.147347484 Reorder the terms: -1.4375 + x = 1.147347484 Solving -1.4375 + x = 1.147347484 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.4375' to each side of the equation. -1.4375 + 1.4375 + x = 1.147347484 + 1.4375 Combine like terms: -1.4375 + 1.4375 = 0.0000 0.0000 + x = 1.147347484 + 1.4375 x = 1.147347484 + 1.4375 Combine like terms: 1.147347484 + 1.4375 = 2.584847484 x = 2.584847484 Simplifying x = 2.584847484Subproblem 2
x + -1.4375 = -1.147347484 Simplifying x + -1.4375 = -1.147347484 Reorder the terms: -1.4375 + x = -1.147347484 Solving -1.4375 + x = -1.147347484 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.4375' to each side of the equation. -1.4375 + 1.4375 + x = -1.147347484 + 1.4375 Combine like terms: -1.4375 + 1.4375 = 0.0000 0.0000 + x = -1.147347484 + 1.4375 x = -1.147347484 + 1.4375 Combine like terms: -1.147347484 + 1.4375 = 0.290152516 x = 0.290152516 Simplifying x = 0.290152516Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.584847484, 0.290152516}
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