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Simplifying f(0) = 2x2 + -6x + 6 Reorder the terms for easier multiplication: 0f = 2x2 + -6x + 6 Anything times zero is zero. 0f = 2x2 + -6x + 6 Reorder the terms: 0 = 6 + -6x + 2x2 Solving 0 = 6 + -6x + 2x2 Solving for variable 'x'. Combine like terms: 0 + -6 = -6 -6 + 6x + -2x2 = 6 + -6x + 2x2 + -6 + 6x + -2x2 Reorder the terms: -6 + 6x + -2x2 = 6 + -6 + -6x + 6x + 2x2 + -2x2 Combine like terms: 6 + -6 = 0 -6 + 6x + -2x2 = 0 + -6x + 6x + 2x2 + -2x2 -6 + 6x + -2x2 = -6x + 6x + 2x2 + -2x2 Combine like terms: -6x + 6x = 0 -6 + 6x + -2x2 = 0 + 2x2 + -2x2 -6 + 6x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -6 + 6x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + 3x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + 3x + -1x2)' equal to zero and attempt to solve: Simplifying -3 + 3x + -1x2 = 0 Solving -3 + 3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 3 + -3x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -3x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -3x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -3x + x2 = 0 + -3 -3x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -3x + x2 = -3 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = -3 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -3 + 2.25 Combine like terms: -3 + 2.25 = -0.75 2.25 + -3x + x2 = -0.75 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = -0.75 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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