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Simplifying x + -1x2 + -6 + 6x = 9 + 24x + 4x2 Reorder the terms: -6 + x + 6x + -1x2 = 9 + 24x + 4x2 Combine like terms: x + 6x = 7x -6 + 7x + -1x2 = 9 + 24x + 4x2 Solving -6 + 7x + -1x2 = 9 + 24x + 4x2 Solving for variable 'x'. Reorder the terms: -6 + -9 + 7x + -24x + -1x2 + -4x2 = 9 + 24x + 4x2 + -9 + -24x + -4x2 Combine like terms: -6 + -9 = -15 -15 + 7x + -24x + -1x2 + -4x2 = 9 + 24x + 4x2 + -9 + -24x + -4x2 Combine like terms: 7x + -24x = -17x -15 + -17x + -1x2 + -4x2 = 9 + 24x + 4x2 + -9 + -24x + -4x2 Combine like terms: -1x2 + -4x2 = -5x2 -15 + -17x + -5x2 = 9 + 24x + 4x2 + -9 + -24x + -4x2 Reorder the terms: -15 + -17x + -5x2 = 9 + -9 + 24x + -24x + 4x2 + -4x2 Combine like terms: 9 + -9 = 0 -15 + -17x + -5x2 = 0 + 24x + -24x + 4x2 + -4x2 -15 + -17x + -5x2 = 24x + -24x + 4x2 + -4x2 Combine like terms: 24x + -24x = 0 -15 + -17x + -5x2 = 0 + 4x2 + -4x2 -15 + -17x + -5x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -15 + -17x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(15 + 17x + 5x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(15 + 17x + 5x2)' equal to zero and attempt to solve: Simplifying 15 + 17x + 5x2 = 0 Solving 15 + 17x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 3 + 3.4x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + 3.4x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 3.4x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 3.4x + x2 = 0 + -3 3.4x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 3.4x + x2 = -3 The x term is 3.4x. Take half its coefficient (1.7). Square it (2.89) and add it to both sides. Add '2.89' to each side of the equation. 3.4x + 2.89 + x2 = -3 + 2.89 Reorder the terms: 2.89 + 3.4x + x2 = -3 + 2.89 Combine like terms: -3 + 2.89 = -0.11 2.89 + 3.4x + x2 = -0.11 Factor a perfect square on the left side: (x + 1.7)(x + 1.7) = -0.11 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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