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Simplifying 3x2 + 45 = 12x Reorder the terms: 45 + 3x2 = 12x Solving 45 + 3x2 = 12x Solving for variable 'x'. Reorder the terms: 45 + -12x + 3x2 = 12x + -12x Combine like terms: 12x + -12x = 0 45 + -12x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(15 + -4x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(15 + -4x + x2)' equal to zero and attempt to solve: Simplifying 15 + -4x + x2 = 0 Solving 15 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + -4x + -15 + x2 = 0 + -15 Reorder the terms: 15 + -15 + -4x + x2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -4x + x2 = 0 + -15 -4x + x2 = 0 + -15 Combine like terms: 0 + -15 = -15 -4x + x2 = -15 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -15 + 4 Reorder the terms: 4 + -4x + x2 = -15 + 4 Combine like terms: -15 + 4 = -11 4 + -4x + x2 = -11 Factor a perfect square on the left side: (x + -2)(x + -2) = -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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