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Simplifying 5x2 + -50x + 165 = 0 Reorder the terms: 165 + -50x + 5x2 = 0 Solving 165 + -50x + 5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(33 + -10x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(33 + -10x + x2)' equal to zero and attempt to solve: Simplifying 33 + -10x + x2 = 0 Solving 33 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-33' to each side of the equation. 33 + -10x + -33 + x2 = 0 + -33 Reorder the terms: 33 + -33 + -10x + x2 = 0 + -33 Combine like terms: 33 + -33 = 0 0 + -10x + x2 = 0 + -33 -10x + x2 = 0 + -33 Combine like terms: 0 + -33 = -33 -10x + x2 = -33 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -33 + 25 Reorder the terms: 25 + -10x + x2 = -33 + 25 Combine like terms: -33 + 25 = -8 25 + -10x + x2 = -8 Factor a perfect square on the left side: (x + -5)(x + -5) = -8 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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