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Simplifying 12x + -36 + -15x2 + -15 = 6x + -6 Reorder the terms: -36 + -15 + 12x + -15x2 = 6x + -6 Combine like terms: -36 + -15 = -51 -51 + 12x + -15x2 = 6x + -6 Reorder the terms: -51 + 12x + -15x2 = -6 + 6x Solving -51 + 12x + -15x2 = -6 + 6x Solving for variable 'x'. Reorder the terms: -51 + 6 + 12x + -6x + -15x2 = -6 + 6x + 6 + -6x Combine like terms: -51 + 6 = -45 -45 + 12x + -6x + -15x2 = -6 + 6x + 6 + -6x Combine like terms: 12x + -6x = 6x -45 + 6x + -15x2 = -6 + 6x + 6 + -6x Reorder the terms: -45 + 6x + -15x2 = -6 + 6 + 6x + -6x Combine like terms: -6 + 6 = 0 -45 + 6x + -15x2 = 0 + 6x + -6x -45 + 6x + -15x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -45 + 6x + -15x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-15 + 2x + -5x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-15 + 2x + -5x2)' equal to zero and attempt to solve: Simplifying -15 + 2x + -5x2 = 0 Solving -15 + 2x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 3 + -0.4x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -0.4x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -0.4x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -0.4x + x2 = 0 + -3 -0.4x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -0.4x + x2 = -3 The x term is -0.4x. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4x + 0.04 + x2 = -3 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = -3 + 0.04 Combine like terms: -3 + 0.04 = -2.96 0.04 + -0.4x + x2 = -2.96 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = -2.96 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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