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Simplifying 12x2 + 24x + 45 = 0 Reorder the terms: 45 + 24x + 12x2 = 0 Solving 45 + 24x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(15 + 8x + 4x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(15 + 8x + 4x2)' equal to zero and attempt to solve: Simplifying 15 + 8x + 4x2 = 0 Solving 15 + 8x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3.75 + 2x + x2 = 0 Move the constant term to the right: Add '-3.75' to each side of the equation. 3.75 + 2x + -3.75 + x2 = 0 + -3.75 Reorder the terms: 3.75 + -3.75 + 2x + x2 = 0 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + 2x + x2 = 0 + -3.75 2x + x2 = 0 + -3.75 Combine like terms: 0 + -3.75 = -3.75 2x + x2 = -3.75 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = -3.75 + 1 Reorder the terms: 1 + 2x + x2 = -3.75 + 1 Combine like terms: -3.75 + 1 = -2.75 1 + 2x + x2 = -2.75 Factor a perfect square on the left side: (x + 1)(x + 1) = -2.75 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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