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Simplifying x2 + 5x + -10 + 5x = 6x + 89 Reorder the terms: -10 + 5x + 5x + x2 = 6x + 89 Combine like terms: 5x + 5x = 10x -10 + 10x + x2 = 6x + 89 Reorder the terms: -10 + 10x + x2 = 89 + 6x Solving -10 + 10x + x2 = 89 + 6x Solving for variable 'x'. Reorder the terms: -10 + -89 + 10x + -6x + x2 = 89 + 6x + -89 + -6x Combine like terms: -10 + -89 = -99 -99 + 10x + -6x + x2 = 89 + 6x + -89 + -6x Combine like terms: 10x + -6x = 4x -99 + 4x + x2 = 89 + 6x + -89 + -6x Reorder the terms: -99 + 4x + x2 = 89 + -89 + 6x + -6x Combine like terms: 89 + -89 = 0 -99 + 4x + x2 = 0 + 6x + -6x -99 + 4x + x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -99 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '99' to each side of the equation. -99 + 4x + 99 + x2 = 0 + 99 Reorder the terms: -99 + 99 + 4x + x2 = 0 + 99 Combine like terms: -99 + 99 = 0 0 + 4x + x2 = 0 + 99 4x + x2 = 0 + 99 Combine like terms: 0 + 99 = 99 4x + x2 = 99 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 99 + 4 Reorder the terms: 4 + 4x + x2 = 99 + 4 Combine like terms: 99 + 4 = 103 4 + 4x + x2 = 103 Factor a perfect square on the left side: (x + 2)(x + 2) = 103 Calculate the square root of the right side: 10.148891565 Break this problem into two subproblems by setting (x + 2) equal to 10.148891565 and -10.148891565.Subproblem 1
x + 2 = 10.148891565 Simplifying x + 2 = 10.148891565 Reorder the terms: 2 + x = 10.148891565 Solving 2 + x = 10.148891565 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 10.148891565 + -2 Combine like terms: 2 + -2 = 0 0 + x = 10.148891565 + -2 x = 10.148891565 + -2 Combine like terms: 10.148891565 + -2 = 8.148891565 x = 8.148891565 Simplifying x = 8.148891565Subproblem 2
x + 2 = -10.148891565 Simplifying x + 2 = -10.148891565 Reorder the terms: 2 + x = -10.148891565 Solving 2 + x = -10.148891565 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -10.148891565 + -2 Combine like terms: 2 + -2 = 0 0 + x = -10.148891565 + -2 x = -10.148891565 + -2 Combine like terms: -10.148891565 + -2 = -12.148891565 x = -12.148891565 Simplifying x = -12.148891565Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.148891565, -12.148891565}
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