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Simplifying 3x(5x + 2) = 9x + -12 Reorder the terms: 3x(2 + 5x) = 9x + -12 (2 * 3x + 5x * 3x) = 9x + -12 (6x + 15x2) = 9x + -12 Reorder the terms: 6x + 15x2 = -12 + 9x Solving 6x + 15x2 = -12 + 9x Solving for variable 'x'. Reorder the terms: 12 + 6x + -9x + 15x2 = -12 + 9x + 12 + -9x Combine like terms: 6x + -9x = -3x 12 + -3x + 15x2 = -12 + 9x + 12 + -9x Reorder the terms: 12 + -3x + 15x2 = -12 + 12 + 9x + -9x Combine like terms: -12 + 12 = 0 12 + -3x + 15x2 = 0 + 9x + -9x 12 + -3x + 15x2 = 9x + -9x Combine like terms: 9x + -9x = 0 12 + -3x + 15x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(4 + -1x + 5x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(4 + -1x + 5x2)' equal to zero and attempt to solve: Simplifying 4 + -1x + 5x2 = 0 Solving 4 + -1x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.8 + -0.2x + x2 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + -0.2x + -0.8 + x2 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + -0.2x + x2 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + -0.2x + x2 = 0 + -0.8 -0.2x + x2 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 -0.2x + x2 = -0.8 The x term is -0.2x. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2x + 0.01 + x2 = -0.8 + 0.01 Reorder the terms: 0.01 + -0.2x + x2 = -0.8 + 0.01 Combine like terms: -0.8 + 0.01 = -0.79 0.01 + -0.2x + x2 = -0.79 Factor a perfect square on the left side: (x + -0.1)(x + -0.1) = -0.79 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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