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Simplifying (x + 10)(x + -5) = (x + 1) Reorder the terms: (10 + x)(x + -5) = (x + 1) Reorder the terms: (10 + x)(-5 + x) = (x + 1) Multiply (10 + x) * (-5 + x) (10(-5 + x) + x(-5 + x)) = (x + 1) ((-5 * 10 + x * 10) + x(-5 + x)) = (x + 1) ((-50 + 10x) + x(-5 + x)) = (x + 1) (-50 + 10x + (-5 * x + x * x)) = (x + 1) (-50 + 10x + (-5x + x2)) = (x + 1) Combine like terms: 10x + -5x = 5x (-50 + 5x + x2) = (x + 1) Reorder the terms: -50 + 5x + x2 = (1 + x) Remove parenthesis around (1 + x) -50 + 5x + x2 = 1 + x Solving -50 + 5x + x2 = 1 + x Solving for variable 'x'. Reorder the terms: -50 + -1 + 5x + -1x + x2 = 1 + x + -1 + -1x Combine like terms: -50 + -1 = -51 -51 + 5x + -1x + x2 = 1 + x + -1 + -1x Combine like terms: 5x + -1x = 4x -51 + 4x + x2 = 1 + x + -1 + -1x Reorder the terms: -51 + 4x + x2 = 1 + -1 + x + -1x Combine like terms: 1 + -1 = 0 -51 + 4x + x2 = 0 + x + -1x -51 + 4x + x2 = x + -1x Combine like terms: x + -1x = 0 -51 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '51' to each side of the equation. -51 + 4x + 51 + x2 = 0 + 51 Reorder the terms: -51 + 51 + 4x + x2 = 0 + 51 Combine like terms: -51 + 51 = 0 0 + 4x + x2 = 0 + 51 4x + x2 = 0 + 51 Combine like terms: 0 + 51 = 51 4x + x2 = 51 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 = 51 + 4 Reorder the terms: 4 + 4x + x2 = 51 + 4 Combine like terms: 51 + 4 = 55 4 + 4x + x2 = 55 Factor a perfect square on the left side: (x + 2)(x + 2) = 55 Calculate the square root of the right side: 7.416198487 Break this problem into two subproblems by setting (x + 2) equal to 7.416198487 and -7.416198487.Subproblem 1
x + 2 = 7.416198487 Simplifying x + 2 = 7.416198487 Reorder the terms: 2 + x = 7.416198487 Solving 2 + x = 7.416198487 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 = 7.416198487 + -2 Combine like terms: 2 + -2 = 0 0 + x = 7.416198487 + -2 x = 7.416198487 + -2 Combine like terms: 7.416198487 + -2 = 5.416198487 x = 5.416198487 Simplifying x = 5.416198487Subproblem 2
x + 2 = -7.416198487 Simplifying x + 2 = -7.416198487 Reorder the terms: 2 + x = -7.416198487 Solving 2 + x = -7.416198487 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 = -7.416198487 + -2 Combine like terms: 2 + -2 = 0 0 + x = -7.416198487 + -2 x = -7.416198487 + -2 Combine like terms: -7.416198487 + -2 = -9.416198487 x = -9.416198487 Simplifying x = -9.416198487Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.416198487, -9.416198487}
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