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Simplifying x2 + 27x + 37 = 0 Reorder the terms: 37 + 27x + x2 = 0 Solving 37 + 27x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-37' to each side of the equation. 37 + 27x + -37 + x2 = 0 + -37 Reorder the terms: 37 + -37 + 27x + x2 = 0 + -37 Combine like terms: 37 + -37 = 0 0 + 27x + x2 = 0 + -37 27x + x2 = 0 + -37 Combine like terms: 0 + -37 = -37 27x + x2 = -37 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 = -37 + 182.25 Reorder the terms: 182.25 + 27x + x2 = -37 + 182.25 Combine like terms: -37 + 182.25 = 145.25 182.25 + 27x + x2 = 145.25 Factor a perfect square on the left side: (x + 13.5)(x + 13.5) = 145.25 Calculate the square root of the right side: 12.051970793 Break this problem into two subproblems by setting (x + 13.5) equal to 12.051970793 and -12.051970793.Subproblem 1
x + 13.5 = 12.051970793 Simplifying x + 13.5 = 12.051970793 Reorder the terms: 13.5 + x = 12.051970793 Solving 13.5 + x = 12.051970793 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 = 12.051970793 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = 12.051970793 + -13.5 x = 12.051970793 + -13.5 Combine like terms: 12.051970793 + -13.5 = -1.448029207 x = -1.448029207 Simplifying x = -1.448029207Subproblem 2
x + 13.5 = -12.051970793 Simplifying x + 13.5 = -12.051970793 Reorder the terms: 13.5 + x = -12.051970793 Solving 13.5 + x = -12.051970793 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 = -12.051970793 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = -12.051970793 + -13.5 x = -12.051970793 + -13.5 Combine like terms: -12.051970793 + -13.5 = -25.551970793 x = -25.551970793 Simplifying x = -25.551970793Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.448029207, -25.551970793}
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