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Simplifying (2x2 + -6x + -9) + -1(3x2 + -2x + 5) = 0 Reorder the terms: (-9 + -6x + 2x2) + -1(3x2 + -2x + 5) = 0 Remove parenthesis around (-9 + -6x + 2x2) -9 + -6x + 2x2 + -1(3x2 + -2x + 5) = 0 Reorder the terms: -9 + -6x + 2x2 + -1(5 + -2x + 3x2) = 0 -9 + -6x + 2x2 + (5 * -1 + -2x * -1 + 3x2 * -1) = 0 -9 + -6x + 2x2 + (-5 + 2x + -3x2) = 0 Reorder the terms: -9 + -5 + -6x + 2x + 2x2 + -3x2 = 0 Combine like terms: -9 + -5 = -14 -14 + -6x + 2x + 2x2 + -3x2 = 0 Combine like terms: -6x + 2x = -4x -14 + -4x + 2x2 + -3x2 = 0 Combine like terms: 2x2 + -3x2 = -1x2 -14 + -4x + -1x2 = 0 Solving -14 + -4x + -1x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(14 + 4x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(14 + 4x + x2)' equal to zero and attempt to solve: Simplifying 14 + 4x + x2 = 0 Solving 14 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + 4x + -14 + x2 = 0 + -14 Reorder the terms: 14 + -14 + 4x + x2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + 4x + x2 = 0 + -14 4x + x2 = 0 + -14 Combine like terms: 0 + -14 = -14 4x + x2 = -14 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = -14 + 4 Reorder the terms: 4 + 4x + x2 = -14 + 4 Combine like terms: -14 + 4 = -10 4 + 4x + x2 = -10 Factor a perfect square on the left side: (x + 2)(x + 2) = -10 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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