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Simplifying 2x(x + -2) = 200 Reorder the terms: 2x(-2 + x) = 200 (-2 * 2x + x * 2x) = 200 (-4x + 2x2) = 200 Solving -4x + 2x2 = 200 Solving for variable 'x'. Reorder the terms: -200 + -4x + 2x2 = 200 + -200 Combine like terms: 200 + -200 = 0 -200 + -4x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-100 + -2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-100 + -2x + x2)' equal to zero and attempt to solve: Simplifying -100 + -2x + x2 = 0 Solving -100 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + -2x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + -2x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + -2x + x2 = 0 + 100 -2x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 -2x + x2 = 100 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 100 + 1 Reorder the terms: 1 + -2x + x2 = 100 + 1 Combine like terms: 100 + 1 = 101 1 + -2x + x2 = 101 Factor a perfect square on the left side: (x + -1)(x + -1) = 101 Calculate the square root of the right side: 10.049875621 Break this problem into two subproblems by setting (x + -1) equal to 10.049875621 and -10.049875621.Subproblem 1
x + -1 = 10.049875621 Simplifying x + -1 = 10.049875621 Reorder the terms: -1 + x = 10.049875621 Solving -1 + x = 10.049875621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 10.049875621 + 1 Combine like terms: -1 + 1 = 0 0 + x = 10.049875621 + 1 x = 10.049875621 + 1 Combine like terms: 10.049875621 + 1 = 11.049875621 x = 11.049875621 Simplifying x = 11.049875621Subproblem 2
x + -1 = -10.049875621 Simplifying x + -1 = -10.049875621 Reorder the terms: -1 + x = -10.049875621 Solving -1 + x = -10.049875621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -10.049875621 + 1 Combine like terms: -1 + 1 = 0 0 + x = -10.049875621 + 1 x = -10.049875621 + 1 Combine like terms: -10.049875621 + 1 = -9.049875621 x = -9.049875621 Simplifying x = -9.049875621Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.049875621, -9.049875621}Solution
x = {11.049875621, -9.049875621}
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