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Simplifying -27x + 9 + -12x2 = 0 Reorder the terms: 9 + -27x + -12x2 = 0 Solving 9 + -27x + -12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(3 + -9x + -4x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + -9x + -4x2)' equal to zero and attempt to solve: Simplifying 3 + -9x + -4x2 = 0 Solving 3 + -9x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -0.75 + 2.25x + x2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + 2.25x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + 2.25x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + 2.25x + x2 = 0 + 0.75 2.25x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 2.25x + x2 = 0.75 The x term is 2.25x. Take half its coefficient (1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. 2.25x + 1.265625 + x2 = 0.75 + 1.265625 Reorder the terms: 1.265625 + 2.25x + x2 = 0.75 + 1.265625 Combine like terms: 0.75 + 1.265625 = 2.015625 1.265625 + 2.25x + x2 = 2.015625 Factor a perfect square on the left side: (x + 1.125)(x + 1.125) = 2.015625 Calculate the square root of the right side: 1.419727086 Break this problem into two subproblems by setting (x + 1.125) equal to 1.419727086 and -1.419727086.Subproblem 1
x + 1.125 = 1.419727086 Simplifying x + 1.125 = 1.419727086 Reorder the terms: 1.125 + x = 1.419727086 Solving 1.125 + x = 1.419727086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = 1.419727086 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = 1.419727086 + -1.125 x = 1.419727086 + -1.125 Combine like terms: 1.419727086 + -1.125 = 0.294727086 x = 0.294727086 Simplifying x = 0.294727086Subproblem 2
x + 1.125 = -1.419727086 Simplifying x + 1.125 = -1.419727086 Reorder the terms: 1.125 + x = -1.419727086 Solving 1.125 + x = -1.419727086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = -1.419727086 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = -1.419727086 + -1.125 x = -1.419727086 + -1.125 Combine like terms: -1.419727086 + -1.125 = -2.544727086 x = -2.544727086 Simplifying x = -2.544727086Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.294727086, -2.544727086}Solution
x = {0.294727086, -2.544727086}
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