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Simplifying 2x2 + -4x + -1040 = 0 Reorder the terms: -1040 + -4x + 2x2 = 0 Solving -1040 + -4x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-520 + -2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-520 + -2x + x2)' equal to zero and attempt to solve: Simplifying -520 + -2x + x2 = 0 Solving -520 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '520' to each side of the equation. -520 + -2x + 520 + x2 = 0 + 520 Reorder the terms: -520 + 520 + -2x + x2 = 0 + 520 Combine like terms: -520 + 520 = 0 0 + -2x + x2 = 0 + 520 -2x + x2 = 0 + 520 Combine like terms: 0 + 520 = 520 -2x + x2 = 520 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 = 520 + 1 Reorder the terms: 1 + -2x + x2 = 520 + 1 Combine like terms: 520 + 1 = 521 1 + -2x + x2 = 521 Factor a perfect square on the left side: (x + -1)(x + -1) = 521 Calculate the square root of the right side: 22.825424421 Break this problem into two subproblems by setting (x + -1) equal to 22.825424421 and -22.825424421.Subproblem 1
x + -1 = 22.825424421 Simplifying x + -1 = 22.825424421 Reorder the terms: -1 + x = 22.825424421 Solving -1 + x = 22.825424421 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 = 22.825424421 + 1 Combine like terms: -1 + 1 = 0 0 + x = 22.825424421 + 1 x = 22.825424421 + 1 Combine like terms: 22.825424421 + 1 = 23.825424421 x = 23.825424421 Simplifying x = 23.825424421Subproblem 2
x + -1 = -22.825424421 Simplifying x + -1 = -22.825424421 Reorder the terms: -1 + x = -22.825424421 Solving -1 + x = -22.825424421 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 = -22.825424421 + 1 Combine like terms: -1 + 1 = 0 0 + x = -22.825424421 + 1 x = -22.825424421 + 1 Combine like terms: -22.825424421 + 1 = -21.825424421 x = -21.825424421 Simplifying x = -21.825424421Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.825424421, -21.825424421}Solution
x = {23.825424421, -21.825424421}
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