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Simplifying 480 = 48x + -6x2 Solving 480 = 48x + -6x2 Solving for variable 'x'. Reorder the terms: 480 + -48x + 6x2 = 48x + -48x + -6x2 + 6x2 Combine like terms: 48x + -48x = 0 480 + -48x + 6x2 = 0 + -6x2 + 6x2 480 + -48x + 6x2 = -6x2 + 6x2 Combine like terms: -6x2 + 6x2 = 0 480 + -48x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(80 + -8x + x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(80 + -8x + x2)' equal to zero and attempt to solve: Simplifying 80 + -8x + x2 = 0 Solving 80 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-80' to each side of the equation. 80 + -8x + -80 + x2 = 0 + -80 Reorder the terms: 80 + -80 + -8x + x2 = 0 + -80 Combine like terms: 80 + -80 = 0 0 + -8x + x2 = 0 + -80 -8x + x2 = 0 + -80 Combine like terms: 0 + -80 = -80 -8x + x2 = -80 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -80 + 16 Reorder the terms: 16 + -8x + x2 = -80 + 16 Combine like terms: -80 + 16 = -64 16 + -8x + x2 = -64 Factor a perfect square on the left side: (x + -4)(x + -4) = -64 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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