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Simplifying (x + -10)(x * 10) = 200 Reorder the terms: (-10 + x)(x * 10) = 200 Reorder the terms for easier multiplication: (-10 + x)(10x) = 200 Remove parenthesis around (10x) (-10 + x) * 10x = 200 Reorder the terms for easier multiplication: 10x(-10 + x) = 200 (-10 * 10x + x * 10x) = 200 (-100x + 10x2) = 200 Solving -100x + 10x2 = 200 Solving for variable 'x'. Reorder the terms: -200 + -100x + 10x2 = 200 + -200 Combine like terms: 200 + -200 = 0 -200 + -100x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(-20 + -10x + x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-20 + -10x + x2)' equal to zero and attempt to solve: Simplifying -20 + -10x + x2 = 0 Solving -20 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + -10x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + -10x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -10x + x2 = 0 + 20 -10x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 -10x + x2 = 20 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 20 + 25 Reorder the terms: 25 + -10x + x2 = 20 + 25 Combine like terms: 20 + 25 = 45 25 + -10x + x2 = 45 Factor a perfect square on the left side: (x + -5)(x + -5) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (x + -5) equal to 6.708203933 and -6.708203933.Subproblem 1
x + -5 = 6.708203933 Simplifying x + -5 = 6.708203933 Reorder the terms: -5 + x = 6.708203933 Solving -5 + x = 6.708203933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 6.708203933 + 5 Combine like terms: -5 + 5 = 0 0 + x = 6.708203933 + 5 x = 6.708203933 + 5 Combine like terms: 6.708203933 + 5 = 11.708203933 x = 11.708203933 Simplifying x = 11.708203933Subproblem 2
x + -5 = -6.708203933 Simplifying x + -5 = -6.708203933 Reorder the terms: -5 + x = -6.708203933 Solving -5 + x = -6.708203933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -6.708203933 + 5 Combine like terms: -5 + 5 = 0 0 + x = -6.708203933 + 5 x = -6.708203933 + 5 Combine like terms: -6.708203933 + 5 = -1.708203933 x = -1.708203933 Simplifying x = -1.708203933Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.708203933, -1.708203933}Solution
x = {11.708203933, -1.708203933}
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