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Simplifying 21x2 + 37x + 9 = 0 Reorder the terms: 9 + 37x + 21x2 = 0 Solving 9 + 37x + 21x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. 0.4285714286 + 1.761904762x + x2 = 0 Move the constant term to the right: Add '-0.4285714286' to each side of the equation. 0.4285714286 + 1.761904762x + -0.4285714286 + x2 = 0 + -0.4285714286 Reorder the terms: 0.4285714286 + -0.4285714286 + 1.761904762x + x2 = 0 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + 1.761904762x + x2 = 0 + -0.4285714286 1.761904762x + x2 = 0 + -0.4285714286 Combine like terms: 0 + -0.4285714286 = -0.4285714286 1.761904762x + x2 = -0.4285714286 The x term is 1.761904762x. Take half its coefficient (0.880952381). Square it (0.7760770976) and add it to both sides. Add '0.7760770976' to each side of the equation. 1.761904762x + 0.7760770976 + x2 = -0.4285714286 + 0.7760770976 Reorder the terms: 0.7760770976 + 1.761904762x + x2 = -0.4285714286 + 0.7760770976 Combine like terms: -0.4285714286 + 0.7760770976 = 0.347505669 0.7760770976 + 1.761904762x + x2 = 0.347505669 Factor a perfect square on the left side: (x + 0.880952381)(x + 0.880952381) = 0.347505669 Calculate the square root of the right side: 0.589496114 Break this problem into two subproblems by setting (x + 0.880952381) equal to 0.589496114 and -0.589496114.Subproblem 1
x + 0.880952381 = 0.589496114 Simplifying x + 0.880952381 = 0.589496114 Reorder the terms: 0.880952381 + x = 0.589496114 Solving 0.880952381 + x = 0.589496114 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.880952381' to each side of the equation. 0.880952381 + -0.880952381 + x = 0.589496114 + -0.880952381 Combine like terms: 0.880952381 + -0.880952381 = 0.000000000 0.000000000 + x = 0.589496114 + -0.880952381 x = 0.589496114 + -0.880952381 Combine like terms: 0.589496114 + -0.880952381 = -0.291456267 x = -0.291456267 Simplifying x = -0.291456267Subproblem 2
x + 0.880952381 = -0.589496114 Simplifying x + 0.880952381 = -0.589496114 Reorder the terms: 0.880952381 + x = -0.589496114 Solving 0.880952381 + x = -0.589496114 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.880952381' to each side of the equation. 0.880952381 + -0.880952381 + x = -0.589496114 + -0.880952381 Combine like terms: 0.880952381 + -0.880952381 = 0.000000000 0.000000000 + x = -0.589496114 + -0.880952381 x = -0.589496114 + -0.880952381 Combine like terms: -0.589496114 + -0.880952381 = -1.470448495 x = -1.470448495 Simplifying x = -1.470448495Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.291456267, -1.470448495}
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