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Simplifying 162 = 36x + -1(2x * 2x) Reorder the terms for easier multiplication: 162 = 36x + -1(2 * 2x * x) Multiply 2 * 2 162 = 36x + -1(4x * x) Multiply x * x 162 = 36x + -1(4x2) Remove parenthesis around (4x2) 162 = 36x + -1 * 4x2 Multiply -1 * 4 162 = 36x + -4x2 Solving 162 = 36x + -4x2 Solving for variable 'x'. Reorder the terms: 162 + -36x + 4x2 = 36x + -36x + -4x2 + 4x2 Combine like terms: 36x + -36x = 0 162 + -36x + 4x2 = 0 + -4x2 + 4x2 162 + -36x + 4x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 162 + -36x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(81 + -18x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(81 + -18x + 2x2)' equal to zero and attempt to solve: Simplifying 81 + -18x + 2x2 = 0 Solving 81 + -18x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 40.5 + -9x + x2 = 0 Move the constant term to the right: Add '-40.5' to each side of the equation. 40.5 + -9x + -40.5 + x2 = 0 + -40.5 Reorder the terms: 40.5 + -40.5 + -9x + x2 = 0 + -40.5 Combine like terms: 40.5 + -40.5 = 0.0 0.0 + -9x + x2 = 0 + -40.5 -9x + x2 = 0 + -40.5 Combine like terms: 0 + -40.5 = -40.5 -9x + x2 = -40.5 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = -40.5 + 20.25 Reorder the terms: 20.25 + -9x + x2 = -40.5 + 20.25 Combine like terms: -40.5 + 20.25 = -20.25 20.25 + -9x + x2 = -20.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = -20.25 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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