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Simplifying 2x2 + 7x = 194 Reorder the terms: 7x + 2x2 = 194 Solving 7x + 2x2 = 194 Solving for variable 'x'. Reorder the terms: -194 + 7x + 2x2 = 194 + -194 Combine like terms: 194 + -194 = 0 -194 + 7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -97 + 3.5x + x2 = 0 Move the constant term to the right: Add '97' to each side of the equation. -97 + 3.5x + 97 + x2 = 0 + 97 Reorder the terms: -97 + 97 + 3.5x + x2 = 0 + 97 Combine like terms: -97 + 97 = 0 0 + 3.5x + x2 = 0 + 97 3.5x + x2 = 0 + 97 Combine like terms: 0 + 97 = 97 3.5x + x2 = 97 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 97 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 97 + 3.0625 Combine like terms: 97 + 3.0625 = 100.0625 3.0625 + 3.5x + x2 = 100.0625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 100.0625 Calculate the square root of the right side: 10.003124512 Break this problem into two subproblems by setting (x + 1.75) equal to 10.003124512 and -10.003124512.Subproblem 1
x + 1.75 = 10.003124512 Simplifying x + 1.75 = 10.003124512 Reorder the terms: 1.75 + x = 10.003124512 Solving 1.75 + x = 10.003124512 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 10.003124512 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 10.003124512 + -1.75 x = 10.003124512 + -1.75 Combine like terms: 10.003124512 + -1.75 = 8.253124512 x = 8.253124512 Simplifying x = 8.253124512Subproblem 2
x + 1.75 = -10.003124512 Simplifying x + 1.75 = -10.003124512 Reorder the terms: 1.75 + x = -10.003124512 Solving 1.75 + x = -10.003124512 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -10.003124512 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -10.003124512 + -1.75 x = -10.003124512 + -1.75 Combine like terms: -10.003124512 + -1.75 = -11.753124512 x = -11.753124512 Simplifying x = -11.753124512Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.253124512, -11.753124512}
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