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Simplifying 2X2 + 23X + -9.3 = 0 Reorder the terms: -9.3 + 23X + 2X2 = 0 Solving -9.3 + 23X + 2X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4.65 + 11.5X + X2 = 0 Move the constant term to the right: Add '4.65' to each side of the equation. -4.65 + 11.5X + 4.65 + X2 = 0 + 4.65 Reorder the terms: -4.65 + 4.65 + 11.5X + X2 = 0 + 4.65 Combine like terms: -4.65 + 4.65 = 0.00 0.00 + 11.5X + X2 = 0 + 4.65 11.5X + X2 = 0 + 4.65 Combine like terms: 0 + 4.65 = 4.65 11.5X + X2 = 4.65 The X term is 11.5X. Take half its coefficient (5.75). Square it (33.0625) and add it to both sides. Add '33.0625' to each side of the equation. 11.5X + 33.0625 + X2 = 4.65 + 33.0625 Reorder the terms: 33.0625 + 11.5X + X2 = 4.65 + 33.0625 Combine like terms: 4.65 + 33.0625 = 37.7125 33.0625 + 11.5X + X2 = 37.7125 Factor a perfect square on the left side: (X + 5.75)(X + 5.75) = 37.7125 Calculate the square root of the right side: 6.141050399 Break this problem into two subproblems by setting (X + 5.75) equal to 6.141050399 and -6.141050399.Subproblem 1
X + 5.75 = 6.141050399 Simplifying X + 5.75 = 6.141050399 Reorder the terms: 5.75 + X = 6.141050399 Solving 5.75 + X = 6.141050399 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-5.75' to each side of the equation. 5.75 + -5.75 + X = 6.141050399 + -5.75 Combine like terms: 5.75 + -5.75 = 0.00 0.00 + X = 6.141050399 + -5.75 X = 6.141050399 + -5.75 Combine like terms: 6.141050399 + -5.75 = 0.391050399 X = 0.391050399 Simplifying X = 0.391050399Subproblem 2
X + 5.75 = -6.141050399 Simplifying X + 5.75 = -6.141050399 Reorder the terms: 5.75 + X = -6.141050399 Solving 5.75 + X = -6.141050399 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-5.75' to each side of the equation. 5.75 + -5.75 + X = -6.141050399 + -5.75 Combine like terms: 5.75 + -5.75 = 0.00 0.00 + X = -6.141050399 + -5.75 X = -6.141050399 + -5.75 Combine like terms: -6.141050399 + -5.75 = -11.891050399 X = -11.891050399 Simplifying X = -11.891050399Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.391050399, -11.891050399}
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