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Simplifying 16x2 + 49x + 4 = 0 Reorder the terms: 4 + 49x + 16x2 = 0 Solving 4 + 49x + 16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.25 + 3.0625x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 3.0625x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + 3.0625x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 3.0625x + x2 = 0 + -0.25 3.0625x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 3.0625x + x2 = -0.25 The x term is 3.0625x. Take half its coefficient (1.53125). Square it (2.344726563) and add it to both sides. Add '2.344726563' to each side of the equation. 3.0625x + 2.344726563 + x2 = -0.25 + 2.344726563 Reorder the terms: 2.344726563 + 3.0625x + x2 = -0.25 + 2.344726563 Combine like terms: -0.25 + 2.344726563 = 2.094726563 2.344726563 + 3.0625x + x2 = 2.094726563 Factor a perfect square on the left side: (x + 1.53125)(x + 1.53125) = 2.094726563 Calculate the square root of the right side: 1.447317022 Break this problem into two subproblems by setting (x + 1.53125) equal to 1.447317022 and -1.447317022.Subproblem 1
x + 1.53125 = 1.447317022 Simplifying x + 1.53125 = 1.447317022 Reorder the terms: 1.53125 + x = 1.447317022 Solving 1.53125 + x = 1.447317022 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.53125' to each side of the equation. 1.53125 + -1.53125 + x = 1.447317022 + -1.53125 Combine like terms: 1.53125 + -1.53125 = 0.00000 0.00000 + x = 1.447317022 + -1.53125 x = 1.447317022 + -1.53125 Combine like terms: 1.447317022 + -1.53125 = -0.083932978 x = -0.083932978 Simplifying x = -0.083932978Subproblem 2
x + 1.53125 = -1.447317022 Simplifying x + 1.53125 = -1.447317022 Reorder the terms: 1.53125 + x = -1.447317022 Solving 1.53125 + x = -1.447317022 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.53125' to each side of the equation. 1.53125 + -1.53125 + x = -1.447317022 + -1.53125 Combine like terms: 1.53125 + -1.53125 = 0.00000 0.00000 + x = -1.447317022 + -1.53125 x = -1.447317022 + -1.53125 Combine like terms: -1.447317022 + -1.53125 = -2.978567022 x = -2.978567022 Simplifying x = -2.978567022Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.083932978, -2.978567022}
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