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Simplifying (2x + -5)(2x + -5) + -4x + -10(x + 3) = 0 Reorder the terms: (-5 + 2x)(2x + -5) + -4x + -10(x + 3) = 0 Reorder the terms: (-5 + 2x)(-5 + 2x) + -4x + -10(x + 3) = 0 Multiply (-5 + 2x) * (-5 + 2x) (-5(-5 + 2x) + 2x * (-5 + 2x)) + -4x + -10(x + 3) = 0 ((-5 * -5 + 2x * -5) + 2x * (-5 + 2x)) + -4x + -10(x + 3) = 0 ((25 + -10x) + 2x * (-5 + 2x)) + -4x + -10(x + 3) = 0 (25 + -10x + (-5 * 2x + 2x * 2x)) + -4x + -10(x + 3) = 0 (25 + -10x + (-10x + 4x2)) + -4x + -10(x + 3) = 0 Combine like terms: -10x + -10x = -20x (25 + -20x + 4x2) + -4x + -10(x + 3) = 0 Reorder the terms: 25 + -20x + 4x2 + -4x + -10(3 + x) = 0 25 + -20x + 4x2 + -4x + (3 * -10 + x * -10) = 0 25 + -20x + 4x2 + -4x + (-30 + -10x) = 0 Reorder the terms: 25 + -30 + -20x + -4x + -10x + 4x2 = 0 Combine like terms: 25 + -30 = -5 -5 + -20x + -4x + -10x + 4x2 = 0 Combine like terms: -20x + -4x = -24x -5 + -24x + -10x + 4x2 = 0 Combine like terms: -24x + -10x = -34x -5 + -34x + 4x2 = 0 Solving -5 + -34x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.25 + -8.5x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -8.5x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -8.5x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -8.5x + x2 = 0 + 1.25 -8.5x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -8.5x + x2 = 1.25 The x term is -8.5x. Take half its coefficient (-4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. -8.5x + 18.0625 + x2 = 1.25 + 18.0625 Reorder the terms: 18.0625 + -8.5x + x2 = 1.25 + 18.0625 Combine like terms: 1.25 + 18.0625 = 19.3125 18.0625 + -8.5x + x2 = 19.3125 Factor a perfect square on the left side: (x + -4.25)(x + -4.25) = 19.3125 Calculate the square root of the right side: 4.394598958 Break this problem into two subproblems by setting (x + -4.25) equal to 4.394598958 and -4.394598958.Subproblem 1
x + -4.25 = 4.394598958 Simplifying x + -4.25 = 4.394598958 Reorder the terms: -4.25 + x = 4.394598958 Solving -4.25 + x = 4.394598958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x = 4.394598958 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = 4.394598958 + 4.25 x = 4.394598958 + 4.25 Combine like terms: 4.394598958 + 4.25 = 8.644598958 x = 8.644598958 Simplifying x = 8.644598958Subproblem 2
x + -4.25 = -4.394598958 Simplifying x + -4.25 = -4.394598958 Reorder the terms: -4.25 + x = -4.394598958 Solving -4.25 + x = -4.394598958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x = -4.394598958 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = -4.394598958 + 4.25 x = -4.394598958 + 4.25 Combine like terms: -4.394598958 + 4.25 = -0.144598958 x = -0.144598958 Simplifying x = -0.144598958Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.644598958, -0.144598958}
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