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Simplifying 24.53 = x2 + 6.67x Reorder the terms: 24.53 = 6.67x + x2 Solving 24.53 = 6.67x + x2 Solving for variable 'x'. Reorder the terms: 24.53 + -6.67x + -1x2 = 6.67x + -6.67x + x2 + -1x2 Combine like terms: 6.67x + -6.67x = 0.00 24.53 + -6.67x + -1x2 = 0.00 + x2 + -1x2 24.53 + -6.67x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 24.53 + -6.67x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -24.53 + 6.67x + x2 = 0 Move the constant term to the right: Add '24.53' to each side of the equation. -24.53 + 6.67x + 24.53 + x2 = 0 + 24.53 Reorder the terms: -24.53 + 24.53 + 6.67x + x2 = 0 + 24.53 Combine like terms: -24.53 + 24.53 = 0.00 0.00 + 6.67x + x2 = 0 + 24.53 6.67x + x2 = 0 + 24.53 Combine like terms: 0 + 24.53 = 24.53 6.67x + x2 = 24.53 The x term is 6.67x. Take half its coefficient (3.335). Square it (11.122225) and add it to both sides. Add '11.122225' to each side of the equation. 6.67x + 11.122225 + x2 = 24.53 + 11.122225 Reorder the terms: 11.122225 + 6.67x + x2 = 24.53 + 11.122225 Combine like terms: 24.53 + 11.122225 = 35.652225 11.122225 + 6.67x + x2 = 35.652225 Factor a perfect square on the left side: (x + 3.335)(x + 3.335) = 35.652225 Calculate the square root of the right side: 5.970948417 Break this problem into two subproblems by setting (x + 3.335) equal to 5.970948417 and -5.970948417.Subproblem 1
x + 3.335 = 5.970948417 Simplifying x + 3.335 = 5.970948417 Reorder the terms: 3.335 + x = 5.970948417 Solving 3.335 + x = 5.970948417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.335' to each side of the equation. 3.335 + -3.335 + x = 5.970948417 + -3.335 Combine like terms: 3.335 + -3.335 = 0.000 0.000 + x = 5.970948417 + -3.335 x = 5.970948417 + -3.335 Combine like terms: 5.970948417 + -3.335 = 2.635948417 x = 2.635948417 Simplifying x = 2.635948417Subproblem 2
x + 3.335 = -5.970948417 Simplifying x + 3.335 = -5.970948417 Reorder the terms: 3.335 + x = -5.970948417 Solving 3.335 + x = -5.970948417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.335' to each side of the equation. 3.335 + -3.335 + x = -5.970948417 + -3.335 Combine like terms: 3.335 + -3.335 = 0.000 0.000 + x = -5.970948417 + -3.335 x = -5.970948417 + -3.335 Combine like terms: -5.970948417 + -3.335 = -9.305948417 x = -9.305948417 Simplifying x = -9.305948417Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.635948417, -9.305948417}
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