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Simplifying 4x2 + 13x + -5 = 0 Reorder the terms: -5 + 13x + 4x2 = 0 Solving -5 + 13x + 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'. -1.25 + 3.25x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + 3.25x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + 3.25x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + 3.25x + x2 = 0 + 1.25 3.25x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 3.25x + x2 = 1.25 The x term is 3.25x. Take half its coefficient (1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. 3.25x + 2.640625 + x2 = 1.25 + 2.640625 Reorder the terms: 2.640625 + 3.25x + x2 = 1.25 + 2.640625 Combine like terms: 1.25 + 2.640625 = 3.890625 2.640625 + 3.25x + x2 = 3.890625 Factor a perfect square on the left side: (x + 1.625)(x + 1.625) = 3.890625 Calculate the square root of the right side: 1.97246673 Break this problem into two subproblems by setting (x + 1.625) equal to 1.97246673 and -1.97246673.Subproblem 1
x + 1.625 = 1.97246673 Simplifying x + 1.625 = 1.97246673 Reorder the terms: 1.625 + x = 1.97246673 Solving 1.625 + x = 1.97246673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + x = 1.97246673 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = 1.97246673 + -1.625 x = 1.97246673 + -1.625 Combine like terms: 1.97246673 + -1.625 = 0.34746673 x = 0.34746673 Simplifying x = 0.34746673Subproblem 2
x + 1.625 = -1.97246673 Simplifying x + 1.625 = -1.97246673 Reorder the terms: 1.625 + x = -1.97246673 Solving 1.625 + x = -1.97246673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + x = -1.97246673 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = -1.97246673 + -1.625 x = -1.97246673 + -1.625 Combine like terms: -1.97246673 + -1.625 = -3.59746673 x = -3.59746673 Simplifying x = -3.59746673Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.34746673, -3.59746673}
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