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Simplifying (8x2 + -4x + -60) + (7x2 + 6x) = 0 Reorder the terms: (-60 + -4x + 8x2) + (7x2 + 6x) = 0 Remove parenthesis around (-60 + -4x + 8x2) -60 + -4x + 8x2 + (7x2 + 6x) = 0 Reorder the terms: -60 + -4x + 8x2 + (6x + 7x2) = 0 Remove parenthesis around (6x + 7x2) -60 + -4x + 8x2 + 6x + 7x2 = 0 Reorder the terms: -60 + -4x + 6x + 8x2 + 7x2 = 0 Combine like terms: -4x + 6x = 2x -60 + 2x + 8x2 + 7x2 = 0 Combine like terms: 8x2 + 7x2 = 15x2 -60 + 2x + 15x2 = 0 Solving -60 + 2x + 15x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -4 + 0.1333333333x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 0.1333333333x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 0.1333333333x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 0.1333333333x + x2 = 0 + 4 0.1333333333x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 0.1333333333x + x2 = 4 The x term is 0.1333333333x. Take half its coefficient (0.06666666665). Square it (0.004444444442) and add it to both sides. Add '0.004444444442' to each side of the equation. 0.1333333333x + 0.004444444442 + x2 = 4 + 0.004444444442 Reorder the terms: 0.004444444442 + 0.1333333333x + x2 = 4 + 0.004444444442 Combine like terms: 4 + 0.004444444442 = 4.004444444442 0.004444444442 + 0.1333333333x + x2 = 4.004444444442 Factor a perfect square on the left side: (x + 0.06666666665)(x + 0.06666666665) = 4.004444444442 Calculate the square root of the right side: 2.001110803 Break this problem into two subproblems by setting (x + 0.06666666665) equal to 2.001110803 and -2.001110803.Subproblem 1
x + 0.06666666665 = 2.001110803 Simplifying x + 0.06666666665 = 2.001110803 Reorder the terms: 0.06666666665 + x = 2.001110803 Solving 0.06666666665 + x = 2.001110803 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.06666666665' to each side of the equation. 0.06666666665 + -0.06666666665 + x = 2.001110803 + -0.06666666665 Combine like terms: 0.06666666665 + -0.06666666665 = 0.00000000000 0.00000000000 + x = 2.001110803 + -0.06666666665 x = 2.001110803 + -0.06666666665 Combine like terms: 2.001110803 + -0.06666666665 = 1.93444413635 x = 1.93444413635 Simplifying x = 1.93444413635Subproblem 2
x + 0.06666666665 = -2.001110803 Simplifying x + 0.06666666665 = -2.001110803 Reorder the terms: 0.06666666665 + x = -2.001110803 Solving 0.06666666665 + x = -2.001110803 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.06666666665' to each side of the equation. 0.06666666665 + -0.06666666665 + x = -2.001110803 + -0.06666666665 Combine like terms: 0.06666666665 + -0.06666666665 = 0.00000000000 0.00000000000 + x = -2.001110803 + -0.06666666665 x = -2.001110803 + -0.06666666665 Combine like terms: -2.001110803 + -0.06666666665 = -2.06777746965 x = -2.06777746965 Simplifying x = -2.06777746965Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.93444413635, -2.06777746965}
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