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Simplifying (x * x) + (x + 5)(x + 5) = 200 Multiply x * x (x2) + (x + 5)(x + 5) = 200 x2 + (x + 5)(x + 5) = 200 Reorder the terms: x2 + (5 + x)(x + 5) = 200 Reorder the terms: x2 + (5 + x)(5 + x) = 200 Multiply (5 + x) * (5 + x) x2 + (5(5 + x) + x(5 + x)) = 200 x2 + ((5 * 5 + x * 5) + x(5 + x)) = 200 x2 + ((25 + 5x) + x(5 + x)) = 200 x2 + (25 + 5x + (5 * x + x * x)) = 200 x2 + (25 + 5x + (5x + x2)) = 200 Combine like terms: 5x + 5x = 10x x2 + (25 + 10x + x2) = 200 Reorder the terms: 25 + 10x + x2 + x2 = 200 Combine like terms: x2 + x2 = 2x2 25 + 10x + 2x2 = 200 Solving 25 + 10x + 2x2 = 200 Solving for variable 'x'. Reorder the terms: 25 + -200 + 10x + 2x2 = 200 + -200 Combine like terms: 25 + -200 = -175 -175 + 10x + 2x2 = 200 + -200 Combine like terms: 200 + -200 = 0 -175 + 10x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -87.5 + 5x + x2 = 0 Move the constant term to the right: Add '87.5' to each side of the equation. -87.5 + 5x + 87.5 + x2 = 0 + 87.5 Reorder the terms: -87.5 + 87.5 + 5x + x2 = 0 + 87.5 Combine like terms: -87.5 + 87.5 = 0.0 0.0 + 5x + x2 = 0 + 87.5 5x + x2 = 0 + 87.5 Combine like terms: 0 + 87.5 = 87.5 5x + x2 = 87.5 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 = 87.5 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 87.5 + 6.25 Combine like terms: 87.5 + 6.25 = 93.75 6.25 + 5x + x2 = 93.75 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 93.75 Calculate the square root of the right side: 9.682458366 Break this problem into two subproblems by setting (x + 2.5) equal to 9.682458366 and -9.682458366.Subproblem 1
x + 2.5 = 9.682458366 Simplifying x + 2.5 = 9.682458366 Reorder the terms: 2.5 + x = 9.682458366 Solving 2.5 + x = 9.682458366 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 = 9.682458366 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 9.682458366 + -2.5 x = 9.682458366 + -2.5 Combine like terms: 9.682458366 + -2.5 = 7.182458366 x = 7.182458366 Simplifying x = 7.182458366Subproblem 2
x + 2.5 = -9.682458366 Simplifying x + 2.5 = -9.682458366 Reorder the terms: 2.5 + x = -9.682458366 Solving 2.5 + x = -9.682458366 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 = -9.682458366 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -9.682458366 + -2.5 x = -9.682458366 + -2.5 Combine like terms: -9.682458366 + -2.5 = -12.182458366 x = -12.182458366 Simplifying x = -12.182458366Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.182458366, -12.182458366}
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