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Simplifying 43.96x + 0.785x2 = 98 Solving 43.96x + 0.785x2 = 98 Solving for variable 'x'. Reorder the terms: -98 + 43.96x + 0.785x2 = 98 + -98 Combine like terms: 98 + -98 = 0 -98 + 43.96x + 0.785x2 = 0 Begin completing the square. Divide all terms by 0.785 the coefficient of the squared term: Divide each side by '0.785'. -124.8407643 + 56x + x2 = 0 Move the constant term to the right: Add '124.8407643' to each side of the equation. -124.8407643 + 56x + 124.8407643 + x2 = 0 + 124.8407643 Reorder the terms: -124.8407643 + 124.8407643 + 56x + x2 = 0 + 124.8407643 Combine like terms: -124.8407643 + 124.8407643 = 0.0000000 0.0000000 + 56x + x2 = 0 + 124.8407643 56x + x2 = 0 + 124.8407643 Combine like terms: 0 + 124.8407643 = 124.8407643 56x + x2 = 124.8407643 The x term is 56x. Take half its coefficient (28). Square it (784) and add it to both sides. Add '784' to each side of the equation. 56x + 784 + x2 = 124.8407643 + 784 Reorder the terms: 784 + 56x + x2 = 124.8407643 + 784 Combine like terms: 124.8407643 + 784 = 908.8407643 784 + 56x + x2 = 908.8407643 Factor a perfect square on the left side: (x + 28)(x + 28) = 908.8407643 Calculate the square root of the right side: 30.14698599 Break this problem into two subproblems by setting (x + 28) equal to 30.14698599 and -30.14698599.Subproblem 1
x + 28 = 30.14698599 Simplifying x + 28 = 30.14698599 Reorder the terms: 28 + x = 30.14698599 Solving 28 + x = 30.14698599 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-28' to each side of the equation. 28 + -28 + x = 30.14698599 + -28 Combine like terms: 28 + -28 = 0 0 + x = 30.14698599 + -28 x = 30.14698599 + -28 Combine like terms: 30.14698599 + -28 = 2.14698599 x = 2.14698599 Simplifying x = 2.14698599Subproblem 2
x + 28 = -30.14698599 Simplifying x + 28 = -30.14698599 Reorder the terms: 28 + x = -30.14698599 Solving 28 + x = -30.14698599 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-28' to each side of the equation. 28 + -28 + x = -30.14698599 + -28 Combine like terms: 28 + -28 = 0 0 + x = -30.14698599 + -28 x = -30.14698599 + -28 Combine like terms: -30.14698599 + -28 = -58.14698599 x = -58.14698599 Simplifying x = -58.14698599Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.14698599, -58.14698599}
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