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Simplifying 2x2 + 5x + -154 = 0 Reorder the terms: -154 + 5x + 2x2 = 0 Solving -154 + 5x + 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 + 2.5x + x2 = 0 Move the constant term to the right: Add '77' to each side of the equation. -77 + 2.5x + 77 + x2 = 0 + 77 Reorder the terms: -77 + 77 + 2.5x + x2 = 0 + 77 Combine like terms: -77 + 77 = 0 0 + 2.5x + x2 = 0 + 77 2.5x + x2 = 0 + 77 Combine like terms: 0 + 77 = 77 2.5x + x2 = 77 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 77 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 77 + 1.5625 Combine like terms: 77 + 1.5625 = 78.5625 1.5625 + 2.5x + x2 = 78.5625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 78.5625 Calculate the square root of the right side: 8.863548951 Break this problem into two subproblems by setting (x + 1.25) equal to 8.863548951 and -8.863548951.Subproblem 1
x + 1.25 = 8.863548951 Simplifying x + 1.25 = 8.863548951 Reorder the terms: 1.25 + x = 8.863548951 Solving 1.25 + x = 8.863548951 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 8.863548951 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 8.863548951 + -1.25 x = 8.863548951 + -1.25 Combine like terms: 8.863548951 + -1.25 = 7.613548951 x = 7.613548951 Simplifying x = 7.613548951Subproblem 2
x + 1.25 = -8.863548951 Simplifying x + 1.25 = -8.863548951 Reorder the terms: 1.25 + x = -8.863548951 Solving 1.25 + x = -8.863548951 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -8.863548951 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -8.863548951 + -1.25 x = -8.863548951 + -1.25 Combine like terms: -8.863548951 + -1.25 = -10.113548951 x = -10.113548951 Simplifying x = -10.113548951Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.613548951, -10.113548951}
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