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Simplifying 27 = 4x + 3x2 Solving 27 = 4x + 3x2 Solving for variable 'x'. Reorder the terms: 27 + -4x + -3x2 = 4x + -4x + 3x2 + -3x2 Combine like terms: 4x + -4x = 0 27 + -4x + -3x2 = 0 + 3x2 + -3x2 27 + -4x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 27 + -4x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -9 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + 1.333333333x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + 1.333333333x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 1.333333333x + x2 = 0 + 9 1.333333333x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 1.333333333x + x2 = 9 The x term is 1.333333333x. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333x + 0.4444444442 + x2 = 9 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = 9 + 0.4444444442 Combine like terms: 9 + 0.4444444442 = 9.4444444442 0.4444444442 + 1.333333333x + x2 = 9.4444444442 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 9.4444444442 Calculate the square root of the right side: 3.073181486 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 3.073181486 and -3.073181486.Subproblem 1
x + 0.6666666665 = 3.073181486 Simplifying x + 0.6666666665 = 3.073181486 Reorder the terms: 0.6666666665 + x = 3.073181486 Solving 0.6666666665 + x = 3.073181486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = 3.073181486 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 3.073181486 + -0.6666666665 x = 3.073181486 + -0.6666666665 Combine like terms: 3.073181486 + -0.6666666665 = 2.4065148195 x = 2.4065148195 Simplifying x = 2.4065148195Subproblem 2
x + 0.6666666665 = -3.073181486 Simplifying x + 0.6666666665 = -3.073181486 Reorder the terms: 0.6666666665 + x = -3.073181486 Solving 0.6666666665 + x = -3.073181486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = -3.073181486 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -3.073181486 + -0.6666666665 x = -3.073181486 + -0.6666666665 Combine like terms: -3.073181486 + -0.6666666665 = -3.7398481525 x = -3.7398481525 Simplifying x = -3.7398481525Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.4065148195, -3.7398481525}
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