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Simplifying 5x2 + -10x + 75 = 0 Reorder the terms: 75 + -10x + 5x2 = 0 Solving 75 + -10x + 5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(15 + -2x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(15 + -2x + x2)' equal to zero and attempt to solve: Simplifying 15 + -2x + x2 = 0 Solving 15 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + -2x + -15 + x2 = 0 + -15 Reorder the terms: 15 + -15 + -2x + x2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -2x + x2 = 0 + -15 -2x + x2 = 0 + -15 Combine like terms: 0 + -15 = -15 -2x + x2 = -15 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 = -15 + 1 Reorder the terms: 1 + -2x + x2 = -15 + 1 Combine like terms: -15 + 1 = -14 1 + -2x + x2 = -14 Factor a perfect square on the left side: (x + -1)(x + -1) = -14 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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