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Simplifying 4x2 + 18x + 1 = 0 Reorder the terms: 1 + 18x + 4x2 = 0 Solving 1 + 18x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.25 + 4.5x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 4.5x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + 4.5x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 4.5x + x2 = 0 + -0.25 4.5x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 4.5x + x2 = -0.25 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = -0.25 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = -0.25 + 5.0625 Combine like terms: -0.25 + 5.0625 = 4.8125 5.0625 + 4.5x + x2 = 4.8125 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 4.8125 Calculate the square root of the right side: 2.193741097 Break this problem into two subproblems by setting (x + 2.25) equal to 2.193741097 and -2.193741097.Subproblem 1
x + 2.25 = 2.193741097 Simplifying x + 2.25 = 2.193741097 Reorder the terms: 2.25 + x = 2.193741097 Solving 2.25 + x = 2.193741097 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 2.193741097 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 2.193741097 + -2.25 x = 2.193741097 + -2.25 Combine like terms: 2.193741097 + -2.25 = -0.056258903 x = -0.056258903 Simplifying x = -0.056258903Subproblem 2
x + 2.25 = -2.193741097 Simplifying x + 2.25 = -2.193741097 Reorder the terms: 2.25 + x = -2.193741097 Solving 2.25 + x = -2.193741097 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -2.193741097 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -2.193741097 + -2.25 x = -2.193741097 + -2.25 Combine like terms: -2.193741097 + -2.25 = -4.443741097 x = -4.443741097 Simplifying x = -4.443741097Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.056258903, -4.443741097}
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