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Simplifying x2 + 2x2 + 10x + 25 = 625 Reorder the terms: 25 + 10x + x2 + 2x2 = 625 Combine like terms: x2 + 2x2 = 3x2 25 + 10x + 3x2 = 625 Solving 25 + 10x + 3x2 = 625 Solving for variable 'x'. Reorder the terms: 25 + -625 + 10x + 3x2 = 625 + -625 Combine like terms: 25 + -625 = -600 -600 + 10x + 3x2 = 625 + -625 Combine like terms: 625 + -625 = 0 -600 + 10x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -200 + 3.333333333x + x2 = 0 Move the constant term to the right: Add '200' to each side of the equation. -200 + 3.333333333x + 200 + x2 = 0 + 200 Reorder the terms: -200 + 200 + 3.333333333x + x2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + 3.333333333x + x2 = 0 + 200 3.333333333x + x2 = 0 + 200 Combine like terms: 0 + 200 = 200 3.333333333x + x2 = 200 The x term is 3.333333333x. Take half its coefficient (1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. 3.333333333x + 2.777777779 + x2 = 200 + 2.777777779 Reorder the terms: 2.777777779 + 3.333333333x + x2 = 200 + 2.777777779 Combine like terms: 200 + 2.777777779 = 202.777777779 2.777777779 + 3.333333333x + x2 = 202.777777779 Factor a perfect square on the left side: (x + 1.666666667)(x + 1.666666667) = 202.777777779 Calculate the square root of the right side: 14.240006242 Break this problem into two subproblems by setting (x + 1.666666667) equal to 14.240006242 and -14.240006242.Subproblem 1
x + 1.666666667 = 14.240006242 Simplifying x + 1.666666667 = 14.240006242 Reorder the terms: 1.666666667 + x = 14.240006242 Solving 1.666666667 + x = 14.240006242 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + x = 14.240006242 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = 14.240006242 + -1.666666667 x = 14.240006242 + -1.666666667 Combine like terms: 14.240006242 + -1.666666667 = 12.573339575 x = 12.573339575 Simplifying x = 12.573339575Subproblem 2
x + 1.666666667 = -14.240006242 Simplifying x + 1.666666667 = -14.240006242 Reorder the terms: 1.666666667 + x = -14.240006242 Solving 1.666666667 + x = -14.240006242 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + x = -14.240006242 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = -14.240006242 + -1.666666667 x = -14.240006242 + -1.666666667 Combine like terms: -14.240006242 + -1.666666667 = -15.906672909 x = -15.906672909 Simplifying x = -15.906672909Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.573339575, -15.906672909}
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