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Simplifying 4x2 + 13x = 14 Reorder the terms: 13x + 4x2 = 14 Solving 13x + 4x2 = 14 Solving for variable 'x'. Reorder the terms: -14 + 13x + 4x2 = 14 + -14 Combine like terms: 14 + -14 = 0 -14 + 13x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.5 + 3.25x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + 3.25x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + 3.25x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + 3.25x + x2 = 0 + 3.5 3.25x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 3.25x + x2 = 3.5 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 = 3.5 + 2.640625 Reorder the terms: 2.640625 + 3.25x + x2 = 3.5 + 2.640625 Combine like terms: 3.5 + 2.640625 = 6.140625 2.640625 + 3.25x + x2 = 6.140625 Factor a perfect square on the left side: (x + 1.625)(x + 1.625) = 6.140625 Calculate the square root of the right side: 2.47802845 Break this problem into two subproblems by setting (x + 1.625) equal to 2.47802845 and -2.47802845.Subproblem 1
x + 1.625 = 2.47802845 Simplifying x + 1.625 = 2.47802845 Reorder the terms: 1.625 + x = 2.47802845 Solving 1.625 + x = 2.47802845 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 = 2.47802845 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = 2.47802845 + -1.625 x = 2.47802845 + -1.625 Combine like terms: 2.47802845 + -1.625 = 0.85302845 x = 0.85302845 Simplifying x = 0.85302845Subproblem 2
x + 1.625 = -2.47802845 Simplifying x + 1.625 = -2.47802845 Reorder the terms: 1.625 + x = -2.47802845 Solving 1.625 + x = -2.47802845 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 = -2.47802845 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = -2.47802845 + -1.625 x = -2.47802845 + -1.625 Combine like terms: -2.47802845 + -1.625 = -4.10302845 x = -4.10302845 Simplifying x = -4.10302845Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.85302845, -4.10302845}
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