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Simplifying (-2) = -1x2 + -10x + -12 -2 = -1x2 + -10x + -12 Reorder the terms: -2 = -12 + -10x + -1x2 Solving -2 = -12 + -10x + -1x2 Solving for variable 'x'. Combine like terms: -2 + 12 = 10 10 + 10x + x2 = -12 + -10x + -1x2 + 12 + 10x + x2 Reorder the terms: 10 + 10x + x2 = -12 + 12 + -10x + 10x + -1x2 + x2 Combine like terms: -12 + 12 = 0 10 + 10x + x2 = 0 + -10x + 10x + -1x2 + x2 10 + 10x + x2 = -10x + 10x + -1x2 + x2 Combine like terms: -10x + 10x = 0 10 + 10x + x2 = 0 + -1x2 + x2 10 + 10x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 10 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + 10x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + 10x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 10x + x2 = 0 + -10 10x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 10x + x2 = -10 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 = -10 + 25 Reorder the terms: 25 + 10x + x2 = -10 + 25 Combine like terms: -10 + 25 = 15 25 + 10x + x2 = 15 Factor a perfect square on the left side: (x + 5)(x + 5) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (x + 5) equal to 3.872983346 and -3.872983346.Subproblem 1
x + 5 = 3.872983346 Simplifying x + 5 = 3.872983346 Reorder the terms: 5 + x = 3.872983346 Solving 5 + x = 3.872983346 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 = 3.872983346 + -5 Combine like terms: 5 + -5 = 0 0 + x = 3.872983346 + -5 x = 3.872983346 + -5 Combine like terms: 3.872983346 + -5 = -1.127016654 x = -1.127016654 Simplifying x = -1.127016654Subproblem 2
x + 5 = -3.872983346 Simplifying x + 5 = -3.872983346 Reorder the terms: 5 + x = -3.872983346 Solving 5 + x = -3.872983346 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 = -3.872983346 + -5 Combine like terms: 5 + -5 = 0 0 + x = -3.872983346 + -5 x = -3.872983346 + -5 Combine like terms: -3.872983346 + -5 = -8.872983346 x = -8.872983346 Simplifying x = -8.872983346Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.127016654, -8.872983346}
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