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Simplifying 52 = x2 + 5x Reorder the terms: 52 = 5x + x2 Solving 52 = 5x + x2 Solving for variable 'x'. Reorder the terms: 52 + -5x + -1x2 = 5x + -5x + x2 + -1x2 Combine like terms: 5x + -5x = 0 52 + -5x + -1x2 = 0 + x2 + -1x2 52 + -5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 52 + -5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -52 + 5x + x2 = 0 Move the constant term to the right: Add '52' to each side of the equation. -52 + 5x + 52 + x2 = 0 + 52 Reorder the terms: -52 + 52 + 5x + x2 = 0 + 52 Combine like terms: -52 + 52 = 0 0 + 5x + x2 = 0 + 52 5x + x2 = 0 + 52 Combine like terms: 0 + 52 = 52 5x + x2 = 52 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 52 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 52 + 6.25 Combine like terms: 52 + 6.25 = 58.25 6.25 + 5x + x2 = 58.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 58.25 Calculate the square root of the right side: 7.632168761 Break this problem into two subproblems by setting (x + 2.5) equal to 7.632168761 and -7.632168761.Subproblem 1
x + 2.5 = 7.632168761 Simplifying x + 2.5 = 7.632168761 Reorder the terms: 2.5 + x = 7.632168761 Solving 2.5 + x = 7.632168761 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 7.632168761 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 7.632168761 + -2.5 x = 7.632168761 + -2.5 Combine like terms: 7.632168761 + -2.5 = 5.132168761 x = 5.132168761 Simplifying x = 5.132168761Subproblem 2
x + 2.5 = -7.632168761 Simplifying x + 2.5 = -7.632168761 Reorder the terms: 2.5 + x = -7.632168761 Solving 2.5 + x = -7.632168761 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -7.632168761 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -7.632168761 + -2.5 x = -7.632168761 + -2.5 Combine like terms: -7.632168761 + -2.5 = -10.132168761 x = -10.132168761 Simplifying x = -10.132168761Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.132168761, -10.132168761}
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