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Simplifying x2 + 10x + 25 + x2 = x2 + 26x + 169 Reorder the terms: 25 + 10x + x2 + x2 = x2 + 26x + 169 Combine like terms: x2 + x2 = 2x2 25 + 10x + 2x2 = x2 + 26x + 169 Reorder the terms: 25 + 10x + 2x2 = 169 + 26x + x2 Solving 25 + 10x + 2x2 = 169 + 26x + x2 Solving for variable 'x'. Reorder the terms: 25 + -169 + 10x + -26x + 2x2 + -1x2 = 169 + 26x + x2 + -169 + -26x + -1x2 Combine like terms: 25 + -169 = -144 -144 + 10x + -26x + 2x2 + -1x2 = 169 + 26x + x2 + -169 + -26x + -1x2 Combine like terms: 10x + -26x = -16x -144 + -16x + 2x2 + -1x2 = 169 + 26x + x2 + -169 + -26x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 -144 + -16x + 1x2 = 169 + 26x + x2 + -169 + -26x + -1x2 Reorder the terms: -144 + -16x + 1x2 = 169 + -169 + 26x + -26x + x2 + -1x2 Combine like terms: 169 + -169 = 0 -144 + -16x + 1x2 = 0 + 26x + -26x + x2 + -1x2 -144 + -16x + 1x2 = 26x + -26x + x2 + -1x2 Combine like terms: 26x + -26x = 0 -144 + -16x + 1x2 = 0 + x2 + -1x2 -144 + -16x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -144 + -16x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '144' to each side of the equation. -144 + -16x + 144 + x2 = 0 + 144 Reorder the terms: -144 + 144 + -16x + x2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + -16x + x2 = 0 + 144 -16x + x2 = 0 + 144 Combine like terms: 0 + 144 = 144 -16x + x2 = 144 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = 144 + 64 Reorder the terms: 64 + -16x + x2 = 144 + 64 Combine like terms: 144 + 64 = 208 64 + -16x + x2 = 208 Factor a perfect square on the left side: (x + -8)(x + -8) = 208 Calculate the square root of the right side: 14.422205102 Break this problem into two subproblems by setting (x + -8) equal to 14.422205102 and -14.422205102.Subproblem 1
x + -8 = 14.422205102 Simplifying x + -8 = 14.422205102 Reorder the terms: -8 + x = 14.422205102 Solving -8 + x = 14.422205102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 14.422205102 + 8 Combine like terms: -8 + 8 = 0 0 + x = 14.422205102 + 8 x = 14.422205102 + 8 Combine like terms: 14.422205102 + 8 = 22.422205102 x = 22.422205102 Simplifying x = 22.422205102Subproblem 2
x + -8 = -14.422205102 Simplifying x + -8 = -14.422205102 Reorder the terms: -8 + x = -14.422205102 Solving -8 + x = -14.422205102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -14.422205102 + 8 Combine like terms: -8 + 8 = 0 0 + x = -14.422205102 + 8 x = -14.422205102 + 8 Combine like terms: -14.422205102 + 8 = -6.422205102 x = -6.422205102 Simplifying x = -6.422205102Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.422205102, -6.422205102}
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