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Simplifying x2 + 3x + -77 = 0 Reorder the terms: -77 + 3x + x2 = 0 Solving -77 + 3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '77' to each side of the equation. -77 + 3x + 77 + x2 = 0 + 77 Reorder the terms: -77 + 77 + 3x + x2 = 0 + 77 Combine like terms: -77 + 77 = 0 0 + 3x + x2 = 0 + 77 3x + x2 = 0 + 77 Combine like terms: 0 + 77 = 77 3x + x2 = 77 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 77 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 77 + 2.25 Combine like terms: 77 + 2.25 = 79.25 2.25 + 3x + x2 = 79.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 79.25 Calculate the square root of the right side: 8.902246907 Break this problem into two subproblems by setting (x + 1.5) equal to 8.902246907 and -8.902246907.Subproblem 1
x + 1.5 = 8.902246907 Simplifying x + 1.5 = 8.902246907 Reorder the terms: 1.5 + x = 8.902246907 Solving 1.5 + x = 8.902246907 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 8.902246907 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 8.902246907 + -1.5 x = 8.902246907 + -1.5 Combine like terms: 8.902246907 + -1.5 = 7.402246907 x = 7.402246907 Simplifying x = 7.402246907Subproblem 2
x + 1.5 = -8.902246907 Simplifying x + 1.5 = -8.902246907 Reorder the terms: 1.5 + x = -8.902246907 Solving 1.5 + x = -8.902246907 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -8.902246907 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -8.902246907 + -1.5 x = -8.902246907 + -1.5 Combine like terms: -8.902246907 + -1.5 = -10.402246907 x = -10.402246907 Simplifying x = -10.402246907Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.402246907, -10.402246907}
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