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Simplifying 2x(2x) + -16x + 32 = 0 Remove parenthesis around (2x) 2x * 2x + -16x + 32 = 0 Reorder the terms for easier multiplication: 2 * 2x * x + -16x + 32 = 0 Multiply 2 * 2 4x * x + -16x + 32 = 0 Multiply x * x 4x2 + -16x + 32 = 0 Reorder the terms: 32 + -16x + 4x2 = 0 Solving 32 + -16x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(8 + -4x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(8 + -4x + x2)' equal to zero and attempt to solve: Simplifying 8 + -4x + x2 = 0 Solving 8 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + -4x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + -4x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -4x + x2 = 0 + -8 -4x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 -4x + x2 = -8 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -8 + 4 Reorder the terms: 4 + -4x + x2 = -8 + 4 Combine like terms: -8 + 4 = -4 4 + -4x + x2 = -4 Factor a perfect square on the left side: (x + -2)(x + -2) = -4 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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