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Simplifying 3x + 121 = x2 + 10x + 25 Reorder the terms: 121 + 3x = x2 + 10x + 25 Reorder the terms: 121 + 3x = 25 + 10x + x2 Solving 121 + 3x = 25 + 10x + x2 Solving for variable 'x'. Reorder the terms: 121 + -25 + 3x + -10x + -1x2 = 25 + 10x + x2 + -25 + -10x + -1x2 Combine like terms: 121 + -25 = 96 96 + 3x + -10x + -1x2 = 25 + 10x + x2 + -25 + -10x + -1x2 Combine like terms: 3x + -10x = -7x 96 + -7x + -1x2 = 25 + 10x + x2 + -25 + -10x + -1x2 Reorder the terms: 96 + -7x + -1x2 = 25 + -25 + 10x + -10x + x2 + -1x2 Combine like terms: 25 + -25 = 0 96 + -7x + -1x2 = 0 + 10x + -10x + x2 + -1x2 96 + -7x + -1x2 = 10x + -10x + x2 + -1x2 Combine like terms: 10x + -10x = 0 96 + -7x + -1x2 = 0 + x2 + -1x2 96 + -7x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 96 + -7x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -96 + 7x + x2 = 0 Move the constant term to the right: Add '96' to each side of the equation. -96 + 7x + 96 + x2 = 0 + 96 Reorder the terms: -96 + 96 + 7x + x2 = 0 + 96 Combine like terms: -96 + 96 = 0 0 + 7x + x2 = 0 + 96 7x + x2 = 0 + 96 Combine like terms: 0 + 96 = 96 7x + x2 = 96 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 96 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 96 + 12.25 Combine like terms: 96 + 12.25 = 108.25 12.25 + 7x + x2 = 108.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 108.25 Calculate the square root of the right side: 10.404326023 Break this problem into two subproblems by setting (x + 3.5) equal to 10.404326023 and -10.404326023.Subproblem 1
x + 3.5 = 10.404326023 Simplifying x + 3.5 = 10.404326023 Reorder the terms: 3.5 + x = 10.404326023 Solving 3.5 + x = 10.404326023 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 10.404326023 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 10.404326023 + -3.5 x = 10.404326023 + -3.5 Combine like terms: 10.404326023 + -3.5 = 6.904326023 x = 6.904326023 Simplifying x = 6.904326023Subproblem 2
x + 3.5 = -10.404326023 Simplifying x + 3.5 = -10.404326023 Reorder the terms: 3.5 + x = -10.404326023 Solving 3.5 + x = -10.404326023 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -10.404326023 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -10.404326023 + -3.5 x = -10.404326023 + -3.5 Combine like terms: -10.404326023 + -3.5 = -13.904326023 x = -13.904326023 Simplifying x = -13.904326023Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.904326023, -13.904326023}
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