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Simplifying 2x2 + 7x + -154 = 0 Reorder the terms: -154 + 7x + 2x2 = 0 Solving -154 + 7x + 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 + 3.5x + x2 = 0 Move the constant term to the right: Add '77' to each side of the equation. -77 + 3.5x + 77 + x2 = 0 + 77 Reorder the terms: -77 + 77 + 3.5x + x2 = 0 + 77 Combine like terms: -77 + 77 = 0 0 + 3.5x + x2 = 0 + 77 3.5x + x2 = 0 + 77 Combine like terms: 0 + 77 = 77 3.5x + x2 = 77 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 77 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 77 + 3.0625 Combine like terms: 77 + 3.0625 = 80.0625 3.0625 + 3.5x + x2 = 80.0625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 80.0625 Calculate the square root of the right side: 8.947765084 Break this problem into two subproblems by setting (x + 1.75) equal to 8.947765084 and -8.947765084.Subproblem 1
x + 1.75 = 8.947765084 Simplifying x + 1.75 = 8.947765084 Reorder the terms: 1.75 + x = 8.947765084 Solving 1.75 + x = 8.947765084 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 8.947765084 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 8.947765084 + -1.75 x = 8.947765084 + -1.75 Combine like terms: 8.947765084 + -1.75 = 7.197765084 x = 7.197765084 Simplifying x = 7.197765084Subproblem 2
x + 1.75 = -8.947765084 Simplifying x + 1.75 = -8.947765084 Reorder the terms: 1.75 + x = -8.947765084 Solving 1.75 + x = -8.947765084 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -8.947765084 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -8.947765084 + -1.75 x = -8.947765084 + -1.75 Combine like terms: -8.947765084 + -1.75 = -10.697765084 x = -10.697765084 Simplifying x = -10.697765084Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.197765084, -10.697765084}
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