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Simplifying x2 + 5x + 5x + x = 64 Reorder the terms: 5x + 5x + x + x2 = 64 Combine like terms: 5x + 5x = 10x 10x + x + x2 = 64 Combine like terms: 10x + x = 11x 11x + x2 = 64 Solving 11x + x2 = 64 Solving for variable 'x'. Reorder the terms: -64 + 11x + x2 = 64 + -64 Combine like terms: 64 + -64 = 0 -64 + 11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '64' to each side of the equation. -64 + 11x + 64 + x2 = 0 + 64 Reorder the terms: -64 + 64 + 11x + x2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + 11x + x2 = 0 + 64 11x + x2 = 0 + 64 Combine like terms: 0 + 64 = 64 11x + x2 = 64 The x term is 11x. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x + 30.25 + x2 = 64 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 64 + 30.25 Combine like terms: 64 + 30.25 = 94.25 30.25 + 11x + x2 = 94.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 94.25 Calculate the square root of the right side: 9.708243919 Break this problem into two subproblems by setting (x + 5.5) equal to 9.708243919 and -9.708243919.Subproblem 1
x + 5.5 = 9.708243919 Simplifying x + 5.5 = 9.708243919 Reorder the terms: 5.5 + x = 9.708243919 Solving 5.5 + x = 9.708243919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 9.708243919 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 9.708243919 + -5.5 x = 9.708243919 + -5.5 Combine like terms: 9.708243919 + -5.5 = 4.208243919 x = 4.208243919 Simplifying x = 4.208243919Subproblem 2
x + 5.5 = -9.708243919 Simplifying x + 5.5 = -9.708243919 Reorder the terms: 5.5 + x = -9.708243919 Solving 5.5 + x = -9.708243919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -9.708243919 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -9.708243919 + -5.5 x = -9.708243919 + -5.5 Combine like terms: -9.708243919 + -5.5 = -15.208243919 x = -15.208243919 Simplifying x = -15.208243919Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.208243919, -15.208243919}
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