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Simplifying 4x2 + -36x + 324 = 0 Reorder the terms: 324 + -36x + 4x2 = 0 Solving 324 + -36x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(81 + -9x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(81 + -9x + x2)' equal to zero and attempt to solve: Simplifying 81 + -9x + x2 = 0 Solving 81 + -9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-81' to each side of the equation. 81 + -9x + -81 + x2 = 0 + -81 Reorder the terms: 81 + -81 + -9x + x2 = 0 + -81 Combine like terms: 81 + -81 = 0 0 + -9x + x2 = 0 + -81 -9x + x2 = 0 + -81 Combine like terms: 0 + -81 = -81 -9x + x2 = -81 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 = -81 + 20.25 Reorder the terms: 20.25 + -9x + x2 = -81 + 20.25 Combine like terms: -81 + 20.25 = -60.75 20.25 + -9x + x2 = -60.75 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = -60.75 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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