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Simplifying 5.2x(x + 7) = 32.5 Reorder the terms: 5.2x(7 + x) = 32.5 (7 * 5.2x + x * 5.2x) = 32.5 (36.4x + 5.2x2) = 32.5 Solving 36.4x + 5.2x2 = 32.5 Solving for variable 'x'. Reorder the terms: -32.5 + 36.4x + 5.2x2 = 32.5 + -32.5 Combine like terms: 32.5 + -32.5 = 0.0 -32.5 + 36.4x + 5.2x2 = 0.0 Begin completing the square. Divide all terms by 5.2 the coefficient of the squared term: Divide each side by '5.2'. -6.25 + 7x + x2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + 7x + 6.25 + x2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + 7x + x2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + 7x + x2 = 0 + 6.25 7x + x2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 7x + x2 = 6.25 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 = 6.25 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 6.25 + 12.25 Combine like terms: 6.25 + 12.25 = 18.5 12.25 + 7x + x2 = 18.5 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 18.5 Calculate the square root of the right side: 4.301162634 Break this problem into two subproblems by setting (x + 3.5) equal to 4.301162634 and -4.301162634.Subproblem 1
x + 3.5 = 4.301162634 Simplifying x + 3.5 = 4.301162634 Reorder the terms: 3.5 + x = 4.301162634 Solving 3.5 + x = 4.301162634 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 = 4.301162634 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 4.301162634 + -3.5 x = 4.301162634 + -3.5 Combine like terms: 4.301162634 + -3.5 = 0.801162634 x = 0.801162634 Simplifying x = 0.801162634Subproblem 2
x + 3.5 = -4.301162634 Simplifying x + 3.5 = -4.301162634 Reorder the terms: 3.5 + x = -4.301162634 Solving 3.5 + x = -4.301162634 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 = -4.301162634 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -4.301162634 + -3.5 x = -4.301162634 + -3.5 Combine like terms: -4.301162634 + -3.5 = -7.801162634 x = -7.801162634 Simplifying x = -7.801162634Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.801162634, -7.801162634}
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