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Simplifying 48x2 + 9 = 50x Reorder the terms: 9 + 48x2 = 50x Solving 9 + 48x2 = 50x Solving for variable 'x'. Reorder the terms: 9 + -50x + 48x2 = 50x + -50x Combine like terms: 50x + -50x = 0 9 + -50x + 48x2 = 0 Begin completing the square. Divide all terms by 48 the coefficient of the squared term: Divide each side by '48'. 0.1875 + -1.041666667x + x2 = 0 Move the constant term to the right: Add '-0.1875' to each side of the equation. 0.1875 + -1.041666667x + -0.1875 + x2 = 0 + -0.1875 Reorder the terms: 0.1875 + -0.1875 + -1.041666667x + x2 = 0 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + -1.041666667x + x2 = 0 + -0.1875 -1.041666667x + x2 = 0 + -0.1875 Combine like terms: 0 + -0.1875 = -0.1875 -1.041666667x + x2 = -0.1875 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 = -0.1875 + 0.2712673613 Reorder the terms: 0.2712673613 + -1.041666667x + x2 = -0.1875 + 0.2712673613 Combine like terms: -0.1875 + 0.2712673613 = 0.0837673613 0.2712673613 + -1.041666667x + x2 = 0.0837673613 Factor a perfect square on the left side: (x + -0.5208333335)(x + -0.5208333335) = 0.0837673613 Calculate the square root of the right side: 0.289425917 Break this problem into two subproblems by setting (x + -0.5208333335) equal to 0.289425917 and -0.289425917.Subproblem 1
x + -0.5208333335 = 0.289425917 Simplifying x + -0.5208333335 = 0.289425917 Reorder the terms: -0.5208333335 + x = 0.289425917 Solving -0.5208333335 + x = 0.289425917 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 = 0.289425917 + 0.5208333335 Combine like terms: -0.5208333335 + 0.5208333335 = 0.0000000000 0.0000000000 + x = 0.289425917 + 0.5208333335 x = 0.289425917 + 0.5208333335 Combine like terms: 0.289425917 + 0.5208333335 = 0.8102592505 x = 0.8102592505 Simplifying x = 0.8102592505Subproblem 2
x + -0.5208333335 = -0.289425917 Simplifying x + -0.5208333335 = -0.289425917 Reorder the terms: -0.5208333335 + x = -0.289425917 Solving -0.5208333335 + x = -0.289425917 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 = -0.289425917 + 0.5208333335 Combine like terms: -0.5208333335 + 0.5208333335 = 0.0000000000 0.0000000000 + x = -0.289425917 + 0.5208333335 x = -0.289425917 + 0.5208333335 Combine like terms: -0.289425917 + 0.5208333335 = 0.2314074165 x = 0.2314074165 Simplifying x = 0.2314074165Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8102592505, 0.2314074165}
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