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Simplifying (-5x + -9x2 + -6) + -1(-5x2 + 3 + -1x) = 0 Reorder the terms: (-6 + -5x + -9x2) + -1(-5x2 + 3 + -1x) = 0 Remove parenthesis around (-6 + -5x + -9x2) -6 + -5x + -9x2 + -1(-5x2 + 3 + -1x) = 0 Reorder the terms: -6 + -5x + -9x2 + -1(3 + -1x + -5x2) = 0 -6 + -5x + -9x2 + (3 * -1 + -1x * -1 + -5x2 * -1) = 0 -6 + -5x + -9x2 + (-3 + 1x + 5x2) = 0 Reorder the terms: -6 + -3 + -5x + 1x + -9x2 + 5x2 = 0 Combine like terms: -6 + -3 = -9 -9 + -5x + 1x + -9x2 + 5x2 = 0 Combine like terms: -5x + 1x = -4x -9 + -4x + -9x2 + 5x2 = 0 Combine like terms: -9x2 + 5x2 = -4x2 -9 + -4x + -4x2 = 0 Solving -9 + -4x + -4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(9 + 4x + 4x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(9 + 4x + 4x2)' equal to zero and attempt to solve: Simplifying 9 + 4x + 4x2 = 0 Solving 9 + 4x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.25 + x + x2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + x + -2.25 + x2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + x + x2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x + x2 = 0 + -2.25 x + x2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 x + x2 = -2.25 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. + 0.25 + x2 = -2.25 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = -2.25 + 0.25 Combine like terms: -2.25 + 0.25 = -2 1.25 + x2 = -2 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -2 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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