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Simplifying x2 + -36 + 4x = 3x2 + 9x Reorder the terms: -36 + 4x + x2 = 3x2 + 9x Reorder the terms: -36 + 4x + x2 = 9x + 3x2 Solving -36 + 4x + x2 = 9x + 3x2 Solving for variable 'x'. Reorder the terms: -36 + 4x + -9x + x2 + -3x2 = 9x + 3x2 + -9x + -3x2 Combine like terms: 4x + -9x = -5x -36 + -5x + x2 + -3x2 = 9x + 3x2 + -9x + -3x2 Combine like terms: x2 + -3x2 = -2x2 -36 + -5x + -2x2 = 9x + 3x2 + -9x + -3x2 Reorder the terms: -36 + -5x + -2x2 = 9x + -9x + 3x2 + -3x2 Combine like terms: 9x + -9x = 0 -36 + -5x + -2x2 = 0 + 3x2 + -3x2 -36 + -5x + -2x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -36 + -5x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(36 + 5x + 2x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(36 + 5x + 2x2)' equal to zero and attempt to solve: Simplifying 36 + 5x + 2x2 = 0 Solving 36 + 5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 18 + 2.5x + x2 = 0 Move the constant term to the right: Add '-18' to each side of the equation. 18 + 2.5x + -18 + x2 = 0 + -18 Reorder the terms: 18 + -18 + 2.5x + x2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + 2.5x + x2 = 0 + -18 2.5x + x2 = 0 + -18 Combine like terms: 0 + -18 = -18 2.5x + x2 = -18 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = -18 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = -18 + 1.5625 Combine like terms: -18 + 1.5625 = -16.4375 1.5625 + 2.5x + x2 = -16.4375 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = -16.4375 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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