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Simplifying 24x2 + 25x + -47 = 0 Reorder the terms: -47 + 25x + 24x2 = 0 Solving -47 + 25x + 24x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -1.958333333 + 1.041666667x + x2 = 0 Move the constant term to the right: Add '1.958333333' to each side of the equation. -1.958333333 + 1.041666667x + 1.958333333 + x2 = 0 + 1.958333333 Reorder the terms: -1.958333333 + 1.958333333 + 1.041666667x + x2 = 0 + 1.958333333 Combine like terms: -1.958333333 + 1.958333333 = 0.000000000 0.000000000 + 1.041666667x + x2 = 0 + 1.958333333 1.041666667x + x2 = 0 + 1.958333333 Combine like terms: 0 + 1.958333333 = 1.958333333 1.041666667x + x2 = 1.958333333 The x term is 1.041666667x. Take half its coefficient (0.5208333335). Square it (0.2712673613) and add it to both sides. Add '0.2712673613' to each side of the equation. 1.041666667x + 0.2712673613 + x2 = 1.958333333 + 0.2712673613 Reorder the terms: 0.2712673613 + 1.041666667x + x2 = 1.958333333 + 0.2712673613 Combine like terms: 1.958333333 + 0.2712673613 = 2.2296006943 0.2712673613 + 1.041666667x + x2 = 2.2296006943 Factor a perfect square on the left side: (x + 0.5208333335)(x + 0.5208333335) = 2.2296006943 Calculate the square root of the right side: 1.493184749 Break this problem into two subproblems by setting (x + 0.5208333335) equal to 1.493184749 and -1.493184749.Subproblem 1
x + 0.5208333335 = 1.493184749 Simplifying x + 0.5208333335 = 1.493184749 Reorder the terms: 0.5208333335 + x = 1.493184749 Solving 0.5208333335 + x = 1.493184749 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5208333335' to each side of the equation. 0.5208333335 + -0.5208333335 + x = 1.493184749 + -0.5208333335 Combine like terms: 0.5208333335 + -0.5208333335 = 0.0000000000 0.0000000000 + x = 1.493184749 + -0.5208333335 x = 1.493184749 + -0.5208333335 Combine like terms: 1.493184749 + -0.5208333335 = 0.9723514155 x = 0.9723514155 Simplifying x = 0.9723514155Subproblem 2
x + 0.5208333335 = -1.493184749 Simplifying x + 0.5208333335 = -1.493184749 Reorder the terms: 0.5208333335 + x = -1.493184749 Solving 0.5208333335 + x = -1.493184749 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5208333335' to each side of the equation. 0.5208333335 + -0.5208333335 + x = -1.493184749 + -0.5208333335 Combine like terms: 0.5208333335 + -0.5208333335 = 0.0000000000 0.0000000000 + x = -1.493184749 + -0.5208333335 x = -1.493184749 + -0.5208333335 Combine like terms: -1.493184749 + -0.5208333335 = -2.0140180825 x = -2.0140180825 Simplifying x = -2.0140180825Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9723514155, -2.0140180825}
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