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Simplifying 4x2 + 156x + 1 = 0 Reorder the terms: 1 + 156x + 4x2 = 0 Solving 1 + 156x + 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 + 39x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 39x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + 39x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 39x + x2 = 0 + -0.25 39x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 39x + x2 = -0.25 The x term is 39x. Take half its coefficient (19.5). Square it (380.25) and add it to both sides. Add '380.25' to each side of the equation. 39x + 380.25 + x2 = -0.25 + 380.25 Reorder the terms: 380.25 + 39x + x2 = -0.25 + 380.25 Combine like terms: -0.25 + 380.25 = 380 380.25 + 39x + x2 = 380 Factor a perfect square on the left side: (x + 19.5)(x + 19.5) = 380 Calculate the square root of the right side: 19.49358869 Break this problem into two subproblems by setting (x + 19.5) equal to 19.49358869 and -19.49358869.Subproblem 1
x + 19.5 = 19.49358869 Simplifying x + 19.5 = 19.49358869 Reorder the terms: 19.5 + x = 19.49358869 Solving 19.5 + x = 19.49358869 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-19.5' to each side of the equation. 19.5 + -19.5 + x = 19.49358869 + -19.5 Combine like terms: 19.5 + -19.5 = 0.0 0.0 + x = 19.49358869 + -19.5 x = 19.49358869 + -19.5 Combine like terms: 19.49358869 + -19.5 = -0.00641131 x = -0.00641131 Simplifying x = -0.00641131Subproblem 2
x + 19.5 = -19.49358869 Simplifying x + 19.5 = -19.49358869 Reorder the terms: 19.5 + x = -19.49358869 Solving 19.5 + x = -19.49358869 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-19.5' to each side of the equation. 19.5 + -19.5 + x = -19.49358869 + -19.5 Combine like terms: 19.5 + -19.5 = 0.0 0.0 + x = -19.49358869 + -19.5 x = -19.49358869 + -19.5 Combine like terms: -19.49358869 + -19.5 = -38.99358869 x = -38.99358869 Simplifying x = -38.99358869Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.00641131, -38.99358869}
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