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Simplifying 26x2 + 48x + -9 = 0 Reorder the terms: -9 + 48x + 26x2 = 0 Solving -9 + 48x + 26x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 26 the coefficient of the squared term: Divide each side by '26'. -0.3461538462 + 1.846153846x + x2 = 0 Move the constant term to the right: Add '0.3461538462' to each side of the equation. -0.3461538462 + 1.846153846x + 0.3461538462 + x2 = 0 + 0.3461538462 Reorder the terms: -0.3461538462 + 0.3461538462 + 1.846153846x + x2 = 0 + 0.3461538462 Combine like terms: -0.3461538462 + 0.3461538462 = 0.0000000000 0.0000000000 + 1.846153846x + x2 = 0 + 0.3461538462 1.846153846x + x2 = 0 + 0.3461538462 Combine like terms: 0 + 0.3461538462 = 0.3461538462 1.846153846x + x2 = 0.3461538462 The x term is 1.846153846x. Take half its coefficient (0.923076923). Square it (0.8520710058) and add it to both sides. Add '0.8520710058' to each side of the equation. 1.846153846x + 0.8520710058 + x2 = 0.3461538462 + 0.8520710058 Reorder the terms: 0.8520710058 + 1.846153846x + x2 = 0.3461538462 + 0.8520710058 Combine like terms: 0.3461538462 + 0.8520710058 = 1.198224852 0.8520710058 + 1.846153846x + x2 = 1.198224852 Factor a perfect square on the left side: (x + 0.923076923)(x + 0.923076923) = 1.198224852 Calculate the square root of the right side: 1.094634575 Break this problem into two subproblems by setting (x + 0.923076923) equal to 1.094634575 and -1.094634575.Subproblem 1
x + 0.923076923 = 1.094634575 Simplifying x + 0.923076923 = 1.094634575 Reorder the terms: 0.923076923 + x = 1.094634575 Solving 0.923076923 + x = 1.094634575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.923076923' to each side of the equation. 0.923076923 + -0.923076923 + x = 1.094634575 + -0.923076923 Combine like terms: 0.923076923 + -0.923076923 = 0.000000000 0.000000000 + x = 1.094634575 + -0.923076923 x = 1.094634575 + -0.923076923 Combine like terms: 1.094634575 + -0.923076923 = 0.171557652 x = 0.171557652 Simplifying x = 0.171557652Subproblem 2
x + 0.923076923 = -1.094634575 Simplifying x + 0.923076923 = -1.094634575 Reorder the terms: 0.923076923 + x = -1.094634575 Solving 0.923076923 + x = -1.094634575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.923076923' to each side of the equation. 0.923076923 + -0.923076923 + x = -1.094634575 + -0.923076923 Combine like terms: 0.923076923 + -0.923076923 = 0.000000000 0.000000000 + x = -1.094634575 + -0.923076923 x = -1.094634575 + -0.923076923 Combine like terms: -1.094634575 + -0.923076923 = -2.017711498 x = -2.017711498 Simplifying x = -2.017711498Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.171557652, -2.017711498}
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