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Simplifying (7x2 + -5x + -33) + (8x2 + 7x) = 0 Reorder the terms: (-33 + -5x + 7x2) + (8x2 + 7x) = 0 Remove parenthesis around (-33 + -5x + 7x2) -33 + -5x + 7x2 + (8x2 + 7x) = 0 Reorder the terms: -33 + -5x + 7x2 + (7x + 8x2) = 0 Remove parenthesis around (7x + 8x2) -33 + -5x + 7x2 + 7x + 8x2 = 0 Reorder the terms: -33 + -5x + 7x + 7x2 + 8x2 = 0 Combine like terms: -5x + 7x = 2x -33 + 2x + 7x2 + 8x2 = 0 Combine like terms: 7x2 + 8x2 = 15x2 -33 + 2x + 15x2 = 0 Solving -33 + 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'. -2.2 + 0.1333333333x + x2 = 0 Move the constant term to the right: Add '2.2' to each side of the equation. -2.2 + 0.1333333333x + 2.2 + x2 = 0 + 2.2 Reorder the terms: -2.2 + 2.2 + 0.1333333333x + x2 = 0 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + 0.1333333333x + x2 = 0 + 2.2 0.1333333333x + x2 = 0 + 2.2 Combine like terms: 0 + 2.2 = 2.2 0.1333333333x + x2 = 2.2 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 = 2.2 + 0.004444444442 Reorder the terms: 0.004444444442 + 0.1333333333x + x2 = 2.2 + 0.004444444442 Combine like terms: 2.2 + 0.004444444442 = 2.204444444442 0.004444444442 + 0.1333333333x + x2 = 2.204444444442 Factor a perfect square on the left side: (x + 0.06666666665)(x + 0.06666666665) = 2.204444444442 Calculate the square root of the right side: 1.484737163 Break this problem into two subproblems by setting (x + 0.06666666665) equal to 1.484737163 and -1.484737163.Subproblem 1
x + 0.06666666665 = 1.484737163 Simplifying x + 0.06666666665 = 1.484737163 Reorder the terms: 0.06666666665 + x = 1.484737163 Solving 0.06666666665 + x = 1.484737163 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 = 1.484737163 + -0.06666666665 Combine like terms: 0.06666666665 + -0.06666666665 = 0.00000000000 0.00000000000 + x = 1.484737163 + -0.06666666665 x = 1.484737163 + -0.06666666665 Combine like terms: 1.484737163 + -0.06666666665 = 1.41807049635 x = 1.41807049635 Simplifying x = 1.41807049635Subproblem 2
x + 0.06666666665 = -1.484737163 Simplifying x + 0.06666666665 = -1.484737163 Reorder the terms: 0.06666666665 + x = -1.484737163 Solving 0.06666666665 + x = -1.484737163 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 = -1.484737163 + -0.06666666665 Combine like terms: 0.06666666665 + -0.06666666665 = 0.00000000000 0.00000000000 + x = -1.484737163 + -0.06666666665 x = -1.484737163 + -0.06666666665 Combine like terms: -1.484737163 + -0.06666666665 = -1.55140382965 x = -1.55140382965 Simplifying x = -1.55140382965Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.41807049635, -1.55140382965}
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