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Simplifying 2x(x + 7) = 25 Reorder the terms: 2x(7 + x) = 25 (7 * 2x + x * 2x) = 25 (14x + 2x2) = 25 Solving 14x + 2x2 = 25 Solving for variable 'x'. Reorder the terms: -25 + 14x + 2x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + 14x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -12.5 + 7x + x2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + 7x + 12.5 + x2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + 7x + x2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + 7x + x2 = 0 + 12.5 7x + x2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 7x + x2 = 12.5 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 = 12.5 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 12.5 + 12.25 Combine like terms: 12.5 + 12.25 = 24.75 12.25 + 7x + x2 = 24.75 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 24.75 Calculate the square root of the right side: 4.974937186 Break this problem into two subproblems by setting (x + 3.5) equal to 4.974937186 and -4.974937186.Subproblem 1
x + 3.5 = 4.974937186 Simplifying x + 3.5 = 4.974937186 Reorder the terms: 3.5 + x = 4.974937186 Solving 3.5 + x = 4.974937186 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 = 4.974937186 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 4.974937186 + -3.5 x = 4.974937186 + -3.5 Combine like terms: 4.974937186 + -3.5 = 1.474937186 x = 1.474937186 Simplifying x = 1.474937186Subproblem 2
x + 3.5 = -4.974937186 Simplifying x + 3.5 = -4.974937186 Reorder the terms: 3.5 + x = -4.974937186 Solving 3.5 + x = -4.974937186 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 = -4.974937186 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -4.974937186 + -3.5 x = -4.974937186 + -3.5 Combine like terms: -4.974937186 + -3.5 = -8.474937186 x = -8.474937186 Simplifying x = -8.474937186Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.474937186, -8.474937186}
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