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Simplifying x2 + 27x + -7 = 0 Reorder the terms: -7 + 27x + x2 = 0 Solving -7 + 27x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + 27x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + 27x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 27x + x2 = 0 + 7 27x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 27x + x2 = 7 The x term is 27x. Take half its coefficient (13.5). Square it (182.25) and add it to both sides. Add '182.25' to each side of the equation. 27x + 182.25 + x2 = 7 + 182.25 Reorder the terms: 182.25 + 27x + x2 = 7 + 182.25 Combine like terms: 7 + 182.25 = 189.25 182.25 + 27x + x2 = 189.25 Factor a perfect square on the left side: (x + 13.5)(x + 13.5) = 189.25 Calculate the square root of the right side: 13.756816492 Break this problem into two subproblems by setting (x + 13.5) equal to 13.756816492 and -13.756816492.Subproblem 1
x + 13.5 = 13.756816492 Simplifying x + 13.5 = 13.756816492 Reorder the terms: 13.5 + x = 13.756816492 Solving 13.5 + x = 13.756816492 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.5' to each side of the equation. 13.5 + -13.5 + x = 13.756816492 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = 13.756816492 + -13.5 x = 13.756816492 + -13.5 Combine like terms: 13.756816492 + -13.5 = 0.256816492 x = 0.256816492 Simplifying x = 0.256816492Subproblem 2
x + 13.5 = -13.756816492 Simplifying x + 13.5 = -13.756816492 Reorder the terms: 13.5 + x = -13.756816492 Solving 13.5 + x = -13.756816492 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.5' to each side of the equation. 13.5 + -13.5 + x = -13.756816492 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = -13.756816492 + -13.5 x = -13.756816492 + -13.5 Combine like terms: -13.756816492 + -13.5 = -27.256816492 x = -27.256816492 Simplifying x = -27.256816492Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.256816492, -27.256816492}
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