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Simplifying x2 + x2 + 7x + 49 = 1225 Reorder the terms: 49 + 7x + x2 + x2 = 1225 Combine like terms: x2 + x2 = 2x2 49 + 7x + 2x2 = 1225 Solving 49 + 7x + 2x2 = 1225 Solving for variable 'x'. Reorder the terms: 49 + -1225 + 7x + 2x2 = 1225 + -1225 Combine like terms: 49 + -1225 = -1176 -1176 + 7x + 2x2 = 1225 + -1225 Combine like terms: 1225 + -1225 = 0 -1176 + 7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -588 + 3.5x + x2 = 0 Move the constant term to the right: Add '588' to each side of the equation. -588 + 3.5x + 588 + x2 = 0 + 588 Reorder the terms: -588 + 588 + 3.5x + x2 = 0 + 588 Combine like terms: -588 + 588 = 0 0 + 3.5x + x2 = 0 + 588 3.5x + x2 = 0 + 588 Combine like terms: 0 + 588 = 588 3.5x + x2 = 588 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 = 588 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 588 + 3.0625 Combine like terms: 588 + 3.0625 = 591.0625 3.0625 + 3.5x + x2 = 591.0625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 591.0625 Calculate the square root of the right side: 24.311776982 Break this problem into two subproblems by setting (x + 1.75) equal to 24.311776982 and -24.311776982.Subproblem 1
x + 1.75 = 24.311776982 Simplifying x + 1.75 = 24.311776982 Reorder the terms: 1.75 + x = 24.311776982 Solving 1.75 + x = 24.311776982 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 = 24.311776982 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 24.311776982 + -1.75 x = 24.311776982 + -1.75 Combine like terms: 24.311776982 + -1.75 = 22.561776982 x = 22.561776982 Simplifying x = 22.561776982Subproblem 2
x + 1.75 = -24.311776982 Simplifying x + 1.75 = -24.311776982 Reorder the terms: 1.75 + x = -24.311776982 Solving 1.75 + x = -24.311776982 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 = -24.311776982 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -24.311776982 + -1.75 x = -24.311776982 + -1.75 Combine like terms: -24.311776982 + -1.75 = -26.061776982 x = -26.061776982 Simplifying x = -26.061776982Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.561776982, -26.061776982}
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