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Simplifying (2x + -10) * 2x + (2x + -10) * 5x = 170 Reorder the terms: (-10 + 2x) * 2x + (2x + -10) * 5x = 170 Reorder the terms for easier multiplication: 2x(-10 + 2x) + (2x + -10) * 5x = 170 (-10 * 2x + 2x * 2x) + (2x + -10) * 5x = 170 (-20x + 4x2) + (2x + -10) * 5x = 170 Reorder the terms: -20x + 4x2 + (-10 + 2x) * 5x = 170 Reorder the terms for easier multiplication: -20x + 4x2 + 5x(-10 + 2x) = 170 -20x + 4x2 + (-10 * 5x + 2x * 5x) = 170 -20x + 4x2 + (-50x + 10x2) = 170 Reorder the terms: -20x + -50x + 4x2 + 10x2 = 170 Combine like terms: -20x + -50x = -70x -70x + 4x2 + 10x2 = 170 Combine like terms: 4x2 + 10x2 = 14x2 -70x + 14x2 = 170 Solving -70x + 14x2 = 170 Solving for variable 'x'. Reorder the terms: -170 + -70x + 14x2 = 170 + -170 Combine like terms: 170 + -170 = 0 -170 + -70x + 14x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-85 + -35x + 7x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-85 + -35x + 7x2)' equal to zero and attempt to solve: Simplifying -85 + -35x + 7x2 = 0 Solving -85 + -35x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -12.14285714 + -5x + x2 = 0 Move the constant term to the right: Add '12.14285714' to each side of the equation. -12.14285714 + -5x + 12.14285714 + x2 = 0 + 12.14285714 Reorder the terms: -12.14285714 + 12.14285714 + -5x + x2 = 0 + 12.14285714 Combine like terms: -12.14285714 + 12.14285714 = 0.00000000 0.00000000 + -5x + x2 = 0 + 12.14285714 -5x + x2 = 0 + 12.14285714 Combine like terms: 0 + 12.14285714 = 12.14285714 -5x + x2 = 12.14285714 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 12.14285714 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 12.14285714 + 6.25 Combine like terms: 12.14285714 + 6.25 = 18.39285714 6.25 + -5x + x2 = 18.39285714 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 18.39285714 Calculate the square root of the right side: 4.288689443 Break this problem into two subproblems by setting (x + -2.5) equal to 4.288689443 and -4.288689443.Subproblem 1
x + -2.5 = 4.288689443 Simplifying x + -2.5 = 4.288689443 Reorder the terms: -2.5 + x = 4.288689443 Solving -2.5 + x = 4.288689443 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 4.288689443 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 4.288689443 + 2.5 x = 4.288689443 + 2.5 Combine like terms: 4.288689443 + 2.5 = 6.788689443 x = 6.788689443 Simplifying x = 6.788689443Subproblem 2
x + -2.5 = -4.288689443 Simplifying x + -2.5 = -4.288689443 Reorder the terms: -2.5 + x = -4.288689443 Solving -2.5 + x = -4.288689443 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -4.288689443 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -4.288689443 + 2.5 x = -4.288689443 + 2.5 Combine like terms: -4.288689443 + 2.5 = -1.788689443 x = -1.788689443 Simplifying x = -1.788689443Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.788689443, -1.788689443}Solution
x = {6.788689443, -1.788689443}
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