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Simplifying 5 * 5 + x * x + 5x = 1500 + -26.775 Multiply 5 * 5 25 + x * x + 5x = 1500 + -26.775 Multiply x * x 25 + x2 + 5x = 1500 + -26.775 Reorder the terms: 25 + 5x + x2 = 1500 + -26.775 Combine like terms: 1500 + -26.775 = 1473.225 25 + 5x + x2 = 1473.225 Solving 25 + 5x + x2 = 1473.225 Solving for variable 'x'. Reorder the terms: 25 + -1473.225 + 5x + x2 = 1473.225 + -1473.225 Combine like terms: 25 + -1473.225 = -1448.225 -1448.225 + 5x + x2 = 1473.225 + -1473.225 Combine like terms: 1473.225 + -1473.225 = 0.000 -1448.225 + 5x + x2 = 0.000 Begin completing the square. Move the constant term to the right: Add '1448.225' to each side of the equation. -1448.225 + 5x + 1448.225 + x2 = 0.000 + 1448.225 Reorder the terms: -1448.225 + 1448.225 + 5x + x2 = 0.000 + 1448.225 Combine like terms: -1448.225 + 1448.225 = 0.000 0.000 + 5x + x2 = 0.000 + 1448.225 5x + x2 = 0.000 + 1448.225 Combine like terms: 0.000 + 1448.225 = 1448.225 5x + x2 = 1448.225 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 = 1448.225 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 1448.225 + 6.25 Combine like terms: 1448.225 + 6.25 = 1454.475 6.25 + 5x + x2 = 1454.475 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 1454.475 Calculate the square root of the right side: 38.137579892 Break this problem into two subproblems by setting (x + 2.5) equal to 38.137579892 and -38.137579892.Subproblem 1
x + 2.5 = 38.137579892 Simplifying x + 2.5 = 38.137579892 Reorder the terms: 2.5 + x = 38.137579892 Solving 2.5 + x = 38.137579892 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 = 38.137579892 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 38.137579892 + -2.5 x = 38.137579892 + -2.5 Combine like terms: 38.137579892 + -2.5 = 35.637579892 x = 35.637579892 Simplifying x = 35.637579892Subproblem 2
x + 2.5 = -38.137579892 Simplifying x + 2.5 = -38.137579892 Reorder the terms: 2.5 + x = -38.137579892 Solving 2.5 + x = -38.137579892 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 = -38.137579892 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -38.137579892 + -2.5 x = -38.137579892 + -2.5 Combine like terms: -38.137579892 + -2.5 = -40.637579892 x = -40.637579892 Simplifying x = -40.637579892Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.637579892, -40.637579892}
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