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Simplifying x2 + 10x + 9 = x + -1 Reorder the terms: 9 + 10x + x2 = x + -1 Reorder the terms: 9 + 10x + x2 = -1 + x Solving 9 + 10x + x2 = -1 + x Solving for variable 'x'. Reorder the terms: 9 + 1 + 10x + -1x + x2 = -1 + x + 1 + -1x Combine like terms: 9 + 1 = 10 10 + 10x + -1x + x2 = -1 + x + 1 + -1x Combine like terms: 10x + -1x = 9x 10 + 9x + x2 = -1 + x + 1 + -1x Reorder the terms: 10 + 9x + x2 = -1 + 1 + x + -1x Combine like terms: -1 + 1 = 0 10 + 9x + x2 = 0 + x + -1x 10 + 9x + x2 = x + -1x Combine like terms: x + -1x = 0 10 + 9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + 9x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + 9x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 9x + x2 = 0 + -10 9x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 9x + x2 = -10 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = -10 + 20.25 Reorder the terms: 20.25 + 9x + x2 = -10 + 20.25 Combine like terms: -10 + 20.25 = 10.25 20.25 + 9x + x2 = 10.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (x + 4.5) equal to 3.201562119 and -3.201562119.Subproblem 1
x + 4.5 = 3.201562119 Simplifying x + 4.5 = 3.201562119 Reorder the terms: 4.5 + x = 3.201562119 Solving 4.5 + x = 3.201562119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 3.201562119 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 3.201562119 + -4.5 x = 3.201562119 + -4.5 Combine like terms: 3.201562119 + -4.5 = -1.298437881 x = -1.298437881 Simplifying x = -1.298437881Subproblem 2
x + 4.5 = -3.201562119 Simplifying x + 4.5 = -3.201562119 Reorder the terms: 4.5 + x = -3.201562119 Solving 4.5 + x = -3.201562119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -3.201562119 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -3.201562119 + -4.5 x = -3.201562119 + -4.5 Combine like terms: -3.201562119 + -4.5 = -7.701562119 x = -7.701562119 Simplifying x = -7.701562119Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.298437881, -7.701562119}
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