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Simplifying 4x2 + 0.26503x + 0.00374 = 0 Reorder the terms: 0.00374 + 0.26503x + 4x2 = 0 Solving 0.00374 + 0.26503x + 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'. 0.000935 + 0.0662575x + x2 = 0 Move the constant term to the right: Add '-0.000935' to each side of the equation. 0.000935 + 0.0662575x + -0.000935 + x2 = 0 + -0.000935 Reorder the terms: 0.000935 + -0.000935 + 0.0662575x + x2 = 0 + -0.000935 Combine like terms: 0.000935 + -0.000935 = 0.000000 0.000000 + 0.0662575x + x2 = 0 + -0.000935 0.0662575x + x2 = 0 + -0.000935 Combine like terms: 0 + -0.000935 = -0.000935 0.0662575x + x2 = -0.000935 The x term is 0.0662575x. Take half its coefficient (0.03312875). Square it (0.001097514077) and add it to both sides. Add '0.001097514077' to each side of the equation. 0.0662575x + 0.001097514077 + x2 = -0.000935 + 0.001097514077 Reorder the terms: 0.001097514077 + 0.0662575x + x2 = -0.000935 + 0.001097514077 Combine like terms: -0.000935 + 0.001097514077 = 0.000162514077 0.001097514077 + 0.0662575x + x2 = 0.000162514077 Factor a perfect square on the left side: (x + 0.03312875)(x + 0.03312875) = 0.000162514077 Calculate the square root of the right side: 0.012748101 Break this problem into two subproblems by setting (x + 0.03312875) equal to 0.012748101 and -0.012748101.Subproblem 1
x + 0.03312875 = 0.012748101 Simplifying x + 0.03312875 = 0.012748101 Reorder the terms: 0.03312875 + x = 0.012748101 Solving 0.03312875 + x = 0.012748101 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03312875' to each side of the equation. 0.03312875 + -0.03312875 + x = 0.012748101 + -0.03312875 Combine like terms: 0.03312875 + -0.03312875 = 0.00000000 0.00000000 + x = 0.012748101 + -0.03312875 x = 0.012748101 + -0.03312875 Combine like terms: 0.012748101 + -0.03312875 = -0.020380649 x = -0.020380649 Simplifying x = -0.020380649Subproblem 2
x + 0.03312875 = -0.012748101 Simplifying x + 0.03312875 = -0.012748101 Reorder the terms: 0.03312875 + x = -0.012748101 Solving 0.03312875 + x = -0.012748101 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03312875' to each side of the equation. 0.03312875 + -0.03312875 + x = -0.012748101 + -0.03312875 Combine like terms: 0.03312875 + -0.03312875 = 0.00000000 0.00000000 + x = -0.012748101 + -0.03312875 x = -0.012748101 + -0.03312875 Combine like terms: -0.012748101 + -0.03312875 = -0.045876851 x = -0.045876851 Simplifying x = -0.045876851Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.020380649, -0.045876851}
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