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Simplifying (13x2 + -6x + 11) + -1(9x2 + 24x + -55) = 0 Reorder the terms: (11 + -6x + 13x2) + -1(9x2 + 24x + -55) = 0 Remove parenthesis around (11 + -6x + 13x2) 11 + -6x + 13x2 + -1(9x2 + 24x + -55) = 0 Reorder the terms: 11 + -6x + 13x2 + -1(-55 + 24x + 9x2) = 0 11 + -6x + 13x2 + (-55 * -1 + 24x * -1 + 9x2 * -1) = 0 11 + -6x + 13x2 + (55 + -24x + -9x2) = 0 Reorder the terms: 11 + 55 + -6x + -24x + 13x2 + -9x2 = 0 Combine like terms: 11 + 55 = 66 66 + -6x + -24x + 13x2 + -9x2 = 0 Combine like terms: -6x + -24x = -30x 66 + -30x + 13x2 + -9x2 = 0 Combine like terms: 13x2 + -9x2 = 4x2 66 + -30x + 4x2 = 0 Solving 66 + -30x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(33 + -15x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(33 + -15x + 2x2)' equal to zero and attempt to solve: Simplifying 33 + -15x + 2x2 = 0 Solving 33 + -15x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 16.5 + -7.5x + x2 = 0 Move the constant term to the right: Add '-16.5' to each side of the equation. 16.5 + -7.5x + -16.5 + x2 = 0 + -16.5 Reorder the terms: 16.5 + -16.5 + -7.5x + x2 = 0 + -16.5 Combine like terms: 16.5 + -16.5 = 0.0 0.0 + -7.5x + x2 = 0 + -16.5 -7.5x + x2 = 0 + -16.5 Combine like terms: 0 + -16.5 = -16.5 -7.5x + x2 = -16.5 The x term is -7.5x. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5x + 14.0625 + x2 = -16.5 + 14.0625 Reorder the terms: 14.0625 + -7.5x + x2 = -16.5 + 14.0625 Combine like terms: -16.5 + 14.0625 = -2.4375 14.0625 + -7.5x + x2 = -2.4375 Factor a perfect square on the left side: (x + -3.75)(x + -3.75) = -2.4375 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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