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Simplifying x2 + 0.83x = 144 Reorder the terms: 0.83x + x2 = 144 Solving 0.83x + x2 = 144 Solving for variable 'x'. Reorder the terms: -144 + 0.83x + x2 = 144 + -144 Combine like terms: 144 + -144 = 0 -144 + 0.83x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '144' to each side of the equation. -144 + 0.83x + 144 + x2 = 0 + 144 Reorder the terms: -144 + 144 + 0.83x + x2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + 0.83x + x2 = 0 + 144 0.83x + x2 = 0 + 144 Combine like terms: 0 + 144 = 144 0.83x + x2 = 144 The x term is 0.83x. Take half its coefficient (0.415). Square it (0.172225) and add it to both sides. Add '0.172225' to each side of the equation. 0.83x + 0.172225 + x2 = 144 + 0.172225 Reorder the terms: 0.172225 + 0.83x + x2 = 144 + 0.172225 Combine like terms: 144 + 0.172225 = 144.172225 0.172225 + 0.83x + x2 = 144.172225 Factor a perfect square on the left side: (x + 0.415)(x + 0.415) = 144.172225 Calculate the square root of the right side: 12.007173897 Break this problem into two subproblems by setting (x + 0.415) equal to 12.007173897 and -12.007173897.Subproblem 1
x + 0.415 = 12.007173897 Simplifying x + 0.415 = 12.007173897 Reorder the terms: 0.415 + x = 12.007173897 Solving 0.415 + x = 12.007173897 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.415' to each side of the equation. 0.415 + -0.415 + x = 12.007173897 + -0.415 Combine like terms: 0.415 + -0.415 = 0.000 0.000 + x = 12.007173897 + -0.415 x = 12.007173897 + -0.415 Combine like terms: 12.007173897 + -0.415 = 11.592173897 x = 11.592173897 Simplifying x = 11.592173897Subproblem 2
x + 0.415 = -12.007173897 Simplifying x + 0.415 = -12.007173897 Reorder the terms: 0.415 + x = -12.007173897 Solving 0.415 + x = -12.007173897 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.415' to each side of the equation. 0.415 + -0.415 + x = -12.007173897 + -0.415 Combine like terms: 0.415 + -0.415 = 0.000 0.000 + x = -12.007173897 + -0.415 x = -12.007173897 + -0.415 Combine like terms: -12.007173897 + -0.415 = -12.422173897 x = -12.422173897 Simplifying x = -12.422173897Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.592173897, -12.422173897}
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