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Simplifying (x2 + -5x + -3) + -1(6x2 + 4x + 9) = 0 Reorder the terms: (-3 + -5x + x2) + -1(6x2 + 4x + 9) = 0 Remove parenthesis around (-3 + -5x + x2) -3 + -5x + x2 + -1(6x2 + 4x + 9) = 0 Reorder the terms: -3 + -5x + x2 + -1(9 + 4x + 6x2) = 0 -3 + -5x + x2 + (9 * -1 + 4x * -1 + 6x2 * -1) = 0 -3 + -5x + x2 + (-9 + -4x + -6x2) = 0 Reorder the terms: -3 + -9 + -5x + -4x + x2 + -6x2 = 0 Combine like terms: -3 + -9 = -12 -12 + -5x + -4x + x2 + -6x2 = 0 Combine like terms: -5x + -4x = -9x -12 + -9x + x2 + -6x2 = 0 Combine like terms: x2 + -6x2 = -5x2 -12 + -9x + -5x2 = 0 Solving -12 + -9x + -5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(12 + 9x + 5x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(12 + 9x + 5x2)' equal to zero and attempt to solve: Simplifying 12 + 9x + 5x2 = 0 Solving 12 + 9x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2.4 + 1.8x + x2 = 0 Move the constant term to the right: Add '-2.4' to each side of the equation. 2.4 + 1.8x + -2.4 + x2 = 0 + -2.4 Reorder the terms: 2.4 + -2.4 + 1.8x + x2 = 0 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + 1.8x + x2 = 0 + -2.4 1.8x + x2 = 0 + -2.4 Combine like terms: 0 + -2.4 = -2.4 1.8x + x2 = -2.4 The x term is 1.8x. Take half its coefficient (0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. 1.8x + 0.81 + x2 = -2.4 + 0.81 Reorder the terms: 0.81 + 1.8x + x2 = -2.4 + 0.81 Combine like terms: -2.4 + 0.81 = -1.59 0.81 + 1.8x + x2 = -1.59 Factor a perfect square on the left side: (x + 0.9)(x + 0.9) = -1.59 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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