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Simplifying 16x2 + 47x + -4 = 0 Reorder the terms: -4 + 47x + 16x2 = 0 Solving -4 + 47x + 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 + 2.9375x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + 2.9375x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + 2.9375x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + 2.9375x + x2 = 0 + 0.25 2.9375x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 2.9375x + x2 = 0.25 The x term is 2.9375x. Take half its coefficient (1.46875). Square it (2.157226563) and add it to both sides. Add '2.157226563' to each side of the equation. 2.9375x + 2.157226563 + x2 = 0.25 + 2.157226563 Reorder the terms: 2.157226563 + 2.9375x + x2 = 0.25 + 2.157226563 Combine like terms: 0.25 + 2.157226563 = 2.407226563 2.157226563 + 2.9375x + x2 = 2.407226563 Factor a perfect square on the left side: (x + 1.46875)(x + 1.46875) = 2.407226563 Calculate the square root of the right side: 1.551523949 Break this problem into two subproblems by setting (x + 1.46875) equal to 1.551523949 and -1.551523949.Subproblem 1
x + 1.46875 = 1.551523949 Simplifying x + 1.46875 = 1.551523949 Reorder the terms: 1.46875 + x = 1.551523949 Solving 1.46875 + x = 1.551523949 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.46875' to each side of the equation. 1.46875 + -1.46875 + x = 1.551523949 + -1.46875 Combine like terms: 1.46875 + -1.46875 = 0.00000 0.00000 + x = 1.551523949 + -1.46875 x = 1.551523949 + -1.46875 Combine like terms: 1.551523949 + -1.46875 = 0.082773949 x = 0.082773949 Simplifying x = 0.082773949Subproblem 2
x + 1.46875 = -1.551523949 Simplifying x + 1.46875 = -1.551523949 Reorder the terms: 1.46875 + x = -1.551523949 Solving 1.46875 + x = -1.551523949 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.46875' to each side of the equation. 1.46875 + -1.46875 + x = -1.551523949 + -1.46875 Combine like terms: 1.46875 + -1.46875 = 0.00000 0.00000 + x = -1.551523949 + -1.46875 x = -1.551523949 + -1.46875 Combine like terms: -1.551523949 + -1.46875 = -3.020273949 x = -3.020273949 Simplifying x = -3.020273949Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.082773949, -3.020273949}
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