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Simplifying (3x2 + -2x + 6) + -1(5x2 + 2x + 9) = 0 Reorder the terms: (6 + -2x + 3x2) + -1(5x2 + 2x + 9) = 0 Remove parenthesis around (6 + -2x + 3x2) 6 + -2x + 3x2 + -1(5x2 + 2x + 9) = 0 Reorder the terms: 6 + -2x + 3x2 + -1(9 + 2x + 5x2) = 0 6 + -2x + 3x2 + (9 * -1 + 2x * -1 + 5x2 * -1) = 0 6 + -2x + 3x2 + (-9 + -2x + -5x2) = 0 Reorder the terms: 6 + -9 + -2x + -2x + 3x2 + -5x2 = 0 Combine like terms: 6 + -9 = -3 -3 + -2x + -2x + 3x2 + -5x2 = 0 Combine like terms: -2x + -2x = -4x -3 + -4x + 3x2 + -5x2 = 0 Combine like terms: 3x2 + -5x2 = -2x2 -3 + -4x + -2x2 = 0 Solving -3 + -4x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(3 + 4x + 2x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(3 + 4x + 2x2)' equal to zero and attempt to solve: Simplifying 3 + 4x + 2x2 = 0 Solving 3 + 4x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1.5 + 2x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + 2x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + 2x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + 2x + x2 = 0 + -1.5 2x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 2x + x2 = -1.5 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = -1.5 + 1 Reorder the terms: 1 + 2x + x2 = -1.5 + 1 Combine like terms: -1.5 + 1 = -0.5 1 + 2x + x2 = -0.5 Factor a perfect square on the left side: (x + 1)(x + 1) = -0.5 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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