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Simplifying 5x + 5x + x2 = 64 Combine like terms: 5x + 5x = 10x 10x + x2 = 64 Solving 10x + x2 = 64 Solving for variable 'x'. Reorder the terms: -64 + 10x + x2 = 64 + -64 Combine like terms: 64 + -64 = 0 -64 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '64' to each side of the equation. -64 + 10x + 64 + x2 = 0 + 64 Reorder the terms: -64 + 64 + 10x + x2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + 10x + x2 = 0 + 64 10x + x2 = 0 + 64 Combine like terms: 0 + 64 = 64 10x + x2 = 64 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 = 64 + 25 Reorder the terms: 25 + 10x + x2 = 64 + 25 Combine like terms: 64 + 25 = 89 25 + 10x + x2 = 89 Factor a perfect square on the left side: (x + 5)(x + 5) = 89 Calculate the square root of the right side: 9.433981132 Break this problem into two subproblems by setting (x + 5) equal to 9.433981132 and -9.433981132.Subproblem 1
x + 5 = 9.433981132 Simplifying x + 5 = 9.433981132 Reorder the terms: 5 + x = 9.433981132 Solving 5 + x = 9.433981132 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 = 9.433981132 + -5 Combine like terms: 5 + -5 = 0 0 + x = 9.433981132 + -5 x = 9.433981132 + -5 Combine like terms: 9.433981132 + -5 = 4.433981132 x = 4.433981132 Simplifying x = 4.433981132Subproblem 2
x + 5 = -9.433981132 Simplifying x + 5 = -9.433981132 Reorder the terms: 5 + x = -9.433981132 Solving 5 + x = -9.433981132 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 = -9.433981132 + -5 Combine like terms: 5 + -5 = 0 0 + x = -9.433981132 + -5 x = -9.433981132 + -5 Combine like terms: -9.433981132 + -5 = -14.433981132 x = -14.433981132 Simplifying x = -14.433981132Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.433981132, -14.433981132}
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