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Simplifying 4x2 + 21x + -1 = 0 Reorder the terms: -1 + 21x + 4x2 = 0 Solving -1 + 21x + 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 + 5.25x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + 5.25x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + 5.25x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + 5.25x + x2 = 0 + 0.25 5.25x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 5.25x + x2 = 0.25 The x term is 5.25x. Take half its coefficient (2.625). Square it (6.890625) and add it to both sides. Add '6.890625' to each side of the equation. 5.25x + 6.890625 + x2 = 0.25 + 6.890625 Reorder the terms: 6.890625 + 5.25x + x2 = 0.25 + 6.890625 Combine like terms: 0.25 + 6.890625 = 7.140625 6.890625 + 5.25x + x2 = 7.140625 Factor a perfect square on the left side: (x + 2.625)(x + 2.625) = 7.140625 Calculate the square root of the right side: 2.672194791 Break this problem into two subproblems by setting (x + 2.625) equal to 2.672194791 and -2.672194791.Subproblem 1
x + 2.625 = 2.672194791 Simplifying x + 2.625 = 2.672194791 Reorder the terms: 2.625 + x = 2.672194791 Solving 2.625 + x = 2.672194791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.625' to each side of the equation. 2.625 + -2.625 + x = 2.672194791 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + x = 2.672194791 + -2.625 x = 2.672194791 + -2.625 Combine like terms: 2.672194791 + -2.625 = 0.047194791 x = 0.047194791 Simplifying x = 0.047194791Subproblem 2
x + 2.625 = -2.672194791 Simplifying x + 2.625 = -2.672194791 Reorder the terms: 2.625 + x = -2.672194791 Solving 2.625 + x = -2.672194791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.625' to each side of the equation. 2.625 + -2.625 + x = -2.672194791 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + x = -2.672194791 + -2.625 x = -2.672194791 + -2.625 Combine like terms: -2.672194791 + -2.625 = -5.297194791 x = -5.297194791 Simplifying x = -5.297194791Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.047194791, -5.297194791}
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