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Simplifying 2x2 + 3x + -154 = 0 Reorder the terms: -154 + 3x + 2x2 = 0 Solving -154 + 3x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -77 + 1.5x + x2 = 0 Move the constant term to the right: Add '77' to each side of the equation. -77 + 1.5x + 77 + x2 = 0 + 77 Reorder the terms: -77 + 77 + 1.5x + x2 = 0 + 77 Combine like terms: -77 + 77 = 0 0 + 1.5x + x2 = 0 + 77 1.5x + x2 = 0 + 77 Combine like terms: 0 + 77 = 77 1.5x + x2 = 77 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 77 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 77 + 0.5625 Combine like terms: 77 + 0.5625 = 77.5625 0.5625 + 1.5x + x2 = 77.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 77.5625 Calculate the square root of the right side: 8.806957477 Break this problem into two subproblems by setting (x + 0.75) equal to 8.806957477 and -8.806957477.Subproblem 1
x + 0.75 = 8.806957477 Simplifying x + 0.75 = 8.806957477 Reorder the terms: 0.75 + x = 8.806957477 Solving 0.75 + x = 8.806957477 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 8.806957477 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 8.806957477 + -0.75 x = 8.806957477 + -0.75 Combine like terms: 8.806957477 + -0.75 = 8.056957477 x = 8.056957477 Simplifying x = 8.056957477Subproblem 2
x + 0.75 = -8.806957477 Simplifying x + 0.75 = -8.806957477 Reorder the terms: 0.75 + x = -8.806957477 Solving 0.75 + x = -8.806957477 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -8.806957477 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -8.806957477 + -0.75 x = -8.806957477 + -0.75 Combine like terms: -8.806957477 + -0.75 = -9.556957477 x = -9.556957477 Simplifying x = -9.556957477Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.056957477, -9.556957477}
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