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Simplifying 0 = 5x2 + 12x + 9 Reorder the terms: 0 = 9 + 12x + 5x2 Solving 0 = 9 + 12x + 5x2 Solving for variable 'x'. Combine like terms: 0 + -9 = -9 -9 + -12x + -5x2 = 9 + 12x + 5x2 + -9 + -12x + -5x2 Reorder the terms: -9 + -12x + -5x2 = 9 + -9 + 12x + -12x + 5x2 + -5x2 Combine like terms: 9 + -9 = 0 -9 + -12x + -5x2 = 0 + 12x + -12x + 5x2 + -5x2 -9 + -12x + -5x2 = 12x + -12x + 5x2 + -5x2 Combine like terms: 12x + -12x = 0 -9 + -12x + -5x2 = 0 + 5x2 + -5x2 -9 + -12x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -9 + -12x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(9 + 12x + 5x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(9 + 12x + 5x2)' equal to zero and attempt to solve: Simplifying 9 + 12x + 5x2 = 0 Solving 9 + 12x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.8 + 2.4x + x2 = 0 Move the constant term to the right: Add '-1.8' to each side of the equation. 1.8 + 2.4x + -1.8 + x2 = 0 + -1.8 Reorder the terms: 1.8 + -1.8 + 2.4x + x2 = 0 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + 2.4x + x2 = 0 + -1.8 2.4x + x2 = 0 + -1.8 Combine like terms: 0 + -1.8 = -1.8 2.4x + x2 = -1.8 The x term is 2.4x. Take half its coefficient (1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. 2.4x + 1.44 + x2 = -1.8 + 1.44 Reorder the terms: 1.44 + 2.4x + x2 = -1.8 + 1.44 Combine like terms: -1.8 + 1.44 = -0.36 1.44 + 2.4x + x2 = -0.36 Factor a perfect square on the left side: (x + 1.2)(x + 1.2) = -0.36 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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