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Simplifying 0 = -2x2 + 4x + -100 Reorder the terms: 0 = -100 + 4x + -2x2 Solving 0 = -100 + 4x + -2x2 Solving for variable 'x'. Combine like terms: 0 + 100 = 100 100 + -4x + 2x2 = -100 + 4x + -2x2 + 100 + -4x + 2x2 Reorder the terms: 100 + -4x + 2x2 = -100 + 100 + 4x + -4x + -2x2 + 2x2 Combine like terms: -100 + 100 = 0 100 + -4x + 2x2 = 0 + 4x + -4x + -2x2 + 2x2 100 + -4x + 2x2 = 4x + -4x + -2x2 + 2x2 Combine like terms: 4x + -4x = 0 100 + -4x + 2x2 = 0 + -2x2 + 2x2 100 + -4x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 100 + -4x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(50 + -2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(50 + -2x + x2)' equal to zero and attempt to solve: Simplifying 50 + -2x + x2 = 0 Solving 50 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-50' to each side of the equation. 50 + -2x + -50 + x2 = 0 + -50 Reorder the terms: 50 + -50 + -2x + x2 = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -2x + x2 = 0 + -50 -2x + x2 = 0 + -50 Combine like terms: 0 + -50 = -50 -2x + x2 = -50 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 = -50 + 1 Reorder the terms: 1 + -2x + x2 = -50 + 1 Combine like terms: -50 + 1 = -49 1 + -2x + x2 = -49 Factor a perfect square on the left side: (x + -1)(x + -1) = -49 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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