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Simplifying 2x(x + -2) = 910 Reorder the terms: 2x(-2 + x) = 910 (-2 * 2x + x * 2x) = 910 (-4x + 2x2) = 910 Solving -4x + 2x2 = 910 Solving for variable 'x'. Reorder the terms: -910 + -4x + 2x2 = 910 + -910 Combine like terms: 910 + -910 = 0 -910 + -4x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-455 + -2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-455 + -2x + x2)' equal to zero and attempt to solve: Simplifying -455 + -2x + x2 = 0 Solving -455 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '455' to each side of the equation. -455 + -2x + 455 + x2 = 0 + 455 Reorder the terms: -455 + 455 + -2x + x2 = 0 + 455 Combine like terms: -455 + 455 = 0 0 + -2x + x2 = 0 + 455 -2x + x2 = 0 + 455 Combine like terms: 0 + 455 = 455 -2x + x2 = 455 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 = 455 + 1 Reorder the terms: 1 + -2x + x2 = 455 + 1 Combine like terms: 455 + 1 = 456 1 + -2x + x2 = 456 Factor a perfect square on the left side: (x + -1)(x + -1) = 456 Calculate the square root of the right side: 21.354156504 Break this problem into two subproblems by setting (x + -1) equal to 21.354156504 and -21.354156504.Subproblem 1
x + -1 = 21.354156504 Simplifying x + -1 = 21.354156504 Reorder the terms: -1 + x = 21.354156504 Solving -1 + x = 21.354156504 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 = 21.354156504 + 1 Combine like terms: -1 + 1 = 0 0 + x = 21.354156504 + 1 x = 21.354156504 + 1 Combine like terms: 21.354156504 + 1 = 22.354156504 x = 22.354156504 Simplifying x = 22.354156504Subproblem 2
x + -1 = -21.354156504 Simplifying x + -1 = -21.354156504 Reorder the terms: -1 + x = -21.354156504 Solving -1 + x = -21.354156504 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 = -21.354156504 + 1 Combine like terms: -1 + 1 = 0 0 + x = -21.354156504 + 1 x = -21.354156504 + 1 Combine like terms: -21.354156504 + 1 = -20.354156504 x = -20.354156504 Simplifying x = -20.354156504Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.354156504, -20.354156504}Solution
x = {22.354156504, -20.354156504}
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