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Simplifying 10x + x2 = 425 Solving 10x + x2 = 425 Solving for variable 'x'. Reorder the terms: -425 + 10x + x2 = 425 + -425 Combine like terms: 425 + -425 = 0 -425 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '425' to each side of the equation. -425 + 10x + 425 + x2 = 0 + 425 Reorder the terms: -425 + 425 + 10x + x2 = 0 + 425 Combine like terms: -425 + 425 = 0 0 + 10x + x2 = 0 + 425 10x + x2 = 0 + 425 Combine like terms: 0 + 425 = 425 10x + x2 = 425 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 425 + 25 Reorder the terms: 25 + 10x + x2 = 425 + 25 Combine like terms: 425 + 25 = 450 25 + 10x + x2 = 450 Factor a perfect square on the left side: (x + 5)(x + 5) = 450 Calculate the square root of the right side: 21.213203436 Break this problem into two subproblems by setting (x + 5) equal to 21.213203436 and -21.213203436.Subproblem 1
x + 5 = 21.213203436 Simplifying x + 5 = 21.213203436 Reorder the terms: 5 + x = 21.213203436 Solving 5 + x = 21.213203436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 21.213203436 + -5 Combine like terms: 5 + -5 = 0 0 + x = 21.213203436 + -5 x = 21.213203436 + -5 Combine like terms: 21.213203436 + -5 = 16.213203436 x = 16.213203436 Simplifying x = 16.213203436Subproblem 2
x + 5 = -21.213203436 Simplifying x + 5 = -21.213203436 Reorder the terms: 5 + x = -21.213203436 Solving 5 + x = -21.213203436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -21.213203436 + -5 Combine like terms: 5 + -5 = 0 0 + x = -21.213203436 + -5 x = -21.213203436 + -5 Combine like terms: -21.213203436 + -5 = -26.213203436 x = -26.213203436 Simplifying x = -26.213203436Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.213203436, -26.213203436}
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