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Simplifying -6x2 = 2x + (73 + -1x + 4) + -2 Reorder the terms: -6x2 = 2x + (73 + 4 + -1x) + -2 Combine like terms: 73 + 4 = 77 -6x2 = 2x + (77 + -1x) + -2 Remove parenthesis around (77 + -1x) -6x2 = 2x + 77 + -1x + -2 Reorder the terms: -6x2 = 77 + -2 + 2x + -1x Combine like terms: 77 + -2 = 75 -6x2 = 75 + 2x + -1x Combine like terms: 2x + -1x = 1x -6x2 = 75 + 1x Solving -6x2 = 75 + 1x Solving for variable 'x'. Reorder the terms: -75 + -1x + -6x2 = 75 + 1x + -75 + -1x Reorder the terms: -75 + -1x + -6x2 = 75 + -75 + 1x + -1x Combine like terms: 75 + -75 = 0 -75 + -1x + -6x2 = 0 + 1x + -1x -75 + -1x + -6x2 = 1x + -1x Combine like terms: 1x + -1x = 0 -75 + -1x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(75 + x + 6x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(75 + x + 6x2)' equal to zero and attempt to solve: Simplifying 75 + x + 6x2 = 0 Solving 75 + x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 12.5 + 0.1666666667x + x2 = 0 Move the constant term to the right: Add '-12.5' to each side of the equation. 12.5 + 0.1666666667x + -12.5 + x2 = 0 + -12.5 Reorder the terms: 12.5 + -12.5 + 0.1666666667x + x2 = 0 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + 0.1666666667x + x2 = 0 + -12.5 0.1666666667x + x2 = 0 + -12.5 Combine like terms: 0 + -12.5 = -12.5 0.1666666667x + x2 = -12.5 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.1666666667x + 0.25 + x2 = -12.5 + 0.25 Reorder the terms: 0.25 + 0.1666666667x + x2 = -12.5 + 0.25 Combine like terms: -12.5 + 0.25 = -12.25 0.25 + 0.1666666667x + x2 = -12.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -12.25 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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