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Simplifying -2x2 + -4x + -164 = 0 Reorder the terms: -164 + -4x + -2x2 = 0 Solving -164 + -4x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-2'. -2(82 + 2x + x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(82 + 2x + x2)' equal to zero and attempt to solve: Simplifying 82 + 2x + x2 = 0 Solving 82 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-82' to each side of the equation. 82 + 2x + -82 + x2 = 0 + -82 Reorder the terms: 82 + -82 + 2x + x2 = 0 + -82 Combine like terms: 82 + -82 = 0 0 + 2x + x2 = 0 + -82 2x + x2 = 0 + -82 Combine like terms: 0 + -82 = -82 2x + x2 = -82 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 = -82 + 1 Reorder the terms: 1 + 2x + x2 = -82 + 1 Combine like terms: -82 + 1 = -81 1 + 2x + x2 = -81 Factor a perfect square on the left side: (x + 1)(x + 1) = -81 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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