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Simplifying 5x2 + 3x + -27 = 0 Reorder the terms: -27 + 3x + 5x2 = 0 Solving -27 + 3x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -5.4 + 0.6x + x2 = 0 Move the constant term to the right: Add '5.4' to each side of the equation. -5.4 + 0.6x + 5.4 + x2 = 0 + 5.4 Reorder the terms: -5.4 + 5.4 + 0.6x + x2 = 0 + 5.4 Combine like terms: -5.4 + 5.4 = 0.0 0.0 + 0.6x + x2 = 0 + 5.4 0.6x + x2 = 0 + 5.4 Combine like terms: 0 + 5.4 = 5.4 0.6x + x2 = 5.4 The x term is 0.6x. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6x + 0.09 + x2 = 5.4 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = 5.4 + 0.09 Combine like terms: 5.4 + 0.09 = 5.49 0.09 + 0.6x + x2 = 5.49 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = 5.49 Calculate the square root of the right side: 2.343074903 Break this problem into two subproblems by setting (x + 0.3) equal to 2.343074903 and -2.343074903.Subproblem 1
x + 0.3 = 2.343074903 Simplifying x + 0.3 = 2.343074903 Reorder the terms: 0.3 + x = 2.343074903 Solving 0.3 + x = 2.343074903 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = 2.343074903 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 2.343074903 + -0.3 x = 2.343074903 + -0.3 Combine like terms: 2.343074903 + -0.3 = 2.043074903 x = 2.043074903 Simplifying x = 2.043074903Subproblem 2
x + 0.3 = -2.343074903 Simplifying x + 0.3 = -2.343074903 Reorder the terms: 0.3 + x = -2.343074903 Solving 0.3 + x = -2.343074903 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = -2.343074903 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -2.343074903 + -0.3 x = -2.343074903 + -0.3 Combine like terms: -2.343074903 + -0.3 = -2.643074903 x = -2.643074903 Simplifying x = -2.643074903Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.043074903, -2.643074903}
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