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Simplifying 94 = -2x2 + 4x Reorder the terms: 94 = 4x + -2x2 Solving 94 = 4x + -2x2 Solving for variable 'x'. Reorder the terms: 94 + -4x + 2x2 = 4x + -4x + -2x2 + 2x2 Combine like terms: 4x + -4x = 0 94 + -4x + 2x2 = 0 + -2x2 + 2x2 94 + -4x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 94 + -4x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(47 + -2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(47 + -2x + x2)' equal to zero and attempt to solve: Simplifying 47 + -2x + x2 = 0 Solving 47 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-47' to each side of the equation. 47 + -2x + -47 + x2 = 0 + -47 Reorder the terms: 47 + -47 + -2x + x2 = 0 + -47 Combine like terms: 47 + -47 = 0 0 + -2x + x2 = 0 + -47 -2x + x2 = 0 + -47 Combine like terms: 0 + -47 = -47 -2x + x2 = -47 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 = -47 + 1 Reorder the terms: 1 + -2x + x2 = -47 + 1 Combine like terms: -47 + 1 = -46 1 + -2x + x2 = -46 Factor a perfect square on the left side: (x + -1)(x + -1) = -46 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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