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Simplifying 3x(2 + -3x) = 2x + -27 (2 * 3x + -3x * 3x) = 2x + -27 (6x + -9x2) = 2x + -27 Reorder the terms: 6x + -9x2 = -27 + 2x Solving 6x + -9x2 = -27 + 2x Solving for variable 'x'. Reorder the terms: 27 + 6x + -2x + -9x2 = -27 + 2x + 27 + -2x Combine like terms: 6x + -2x = 4x 27 + 4x + -9x2 = -27 + 2x + 27 + -2x Reorder the terms: 27 + 4x + -9x2 = -27 + 27 + 2x + -2x Combine like terms: -27 + 27 = 0 27 + 4x + -9x2 = 0 + 2x + -2x 27 + 4x + -9x2 = 2x + -2x Combine like terms: 2x + -2x = 0 27 + 4x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -3 + -0.4444444444x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -0.4444444444x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -0.4444444444x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -0.4444444444x + x2 = 0 + 3 -0.4444444444x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -0.4444444444x + x2 = 3 The x term is -0.4444444444x. Take half its coefficient (-0.2222222222). Square it (0.04938271604) and add it to both sides. Add '0.04938271604' to each side of the equation. -0.4444444444x + 0.04938271604 + x2 = 3 + 0.04938271604 Reorder the terms: 0.04938271604 + -0.4444444444x + x2 = 3 + 0.04938271604 Combine like terms: 3 + 0.04938271604 = 3.04938271604 0.04938271604 + -0.4444444444x + x2 = 3.04938271604 Factor a perfect square on the left side: (x + -0.2222222222)(x + -0.2222222222) = 3.04938271604 Calculate the square root of the right side: 1.746248183 Break this problem into two subproblems by setting (x + -0.2222222222) equal to 1.746248183 and -1.746248183.Subproblem 1
x + -0.2222222222 = 1.746248183 Simplifying x + -0.2222222222 = 1.746248183 Reorder the terms: -0.2222222222 + x = 1.746248183 Solving -0.2222222222 + x = 1.746248183 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2222222222' to each side of the equation. -0.2222222222 + 0.2222222222 + x = 1.746248183 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + x = 1.746248183 + 0.2222222222 x = 1.746248183 + 0.2222222222 Combine like terms: 1.746248183 + 0.2222222222 = 1.9684704052 x = 1.9684704052 Simplifying x = 1.9684704052Subproblem 2
x + -0.2222222222 = -1.746248183 Simplifying x + -0.2222222222 = -1.746248183 Reorder the terms: -0.2222222222 + x = -1.746248183 Solving -0.2222222222 + x = -1.746248183 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2222222222' to each side of the equation. -0.2222222222 + 0.2222222222 + x = -1.746248183 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + x = -1.746248183 + 0.2222222222 x = -1.746248183 + 0.2222222222 Combine like terms: -1.746248183 + 0.2222222222 = -1.5240259608 x = -1.5240259608 Simplifying x = -1.5240259608Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.9684704052, -1.5240259608}
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