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Simplifying 36x + 4x * 4x + 81 = x * x Reorder the terms for easier multiplication: 36x + 4 * 4x * x + 81 = x * x Multiply 4 * 4 36x + 16x * x + 81 = x * x Multiply x * x 36x + 16x2 + 81 = x * x Reorder the terms: 81 + 36x + 16x2 = x * x Multiply x * x 81 + 36x + 16x2 = x2 Solving 81 + 36x + 16x2 = x2 Solving for variable 'x'. Combine like terms: 16x2 + -1x2 = 15x2 81 + 36x + 15x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 81 + 36x + 15x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(27 + 12x + 5x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(27 + 12x + 5x2)' equal to zero and attempt to solve: Simplifying 27 + 12x + 5x2 = 0 Solving 27 + 12x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 5.4 + 2.4x + x2 = 0 Move the constant term to the right: Add '-5.4' to each side of the equation. 5.4 + 2.4x + -5.4 + x2 = 0 + -5.4 Reorder the terms: 5.4 + -5.4 + 2.4x + x2 = 0 + -5.4 Combine like terms: 5.4 + -5.4 = 0.0 0.0 + 2.4x + x2 = 0 + -5.4 2.4x + x2 = 0 + -5.4 Combine like terms: 0 + -5.4 = -5.4 2.4x + x2 = -5.4 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 = -5.4 + 1.44 Reorder the terms: 1.44 + 2.4x + x2 = -5.4 + 1.44 Combine like terms: -5.4 + 1.44 = -3.96 1.44 + 2.4x + x2 = -3.96 Factor a perfect square on the left side: (x + 1.2)(x + 1.2) = -3.96 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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