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Simplifying 2x2 + 5x + -176 = 0 Reorder the terms: -176 + 5x + 2x2 = 0 Solving -176 + 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'. -88 + 2.5x + x2 = 0 Move the constant term to the right: Add '88' to each side of the equation. -88 + 2.5x + 88 + x2 = 0 + 88 Reorder the terms: -88 + 88 + 2.5x + x2 = 0 + 88 Combine like terms: -88 + 88 = 0 0 + 2.5x + x2 = 0 + 88 2.5x + x2 = 0 + 88 Combine like terms: 0 + 88 = 88 2.5x + x2 = 88 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 = 88 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 88 + 1.5625 Combine like terms: 88 + 1.5625 = 89.5625 1.5625 + 2.5x + x2 = 89.5625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 89.5625 Calculate the square root of the right side: 9.463746615 Break this problem into two subproblems by setting (x + 1.25) equal to 9.463746615 and -9.463746615.Subproblem 1
x + 1.25 = 9.463746615 Simplifying x + 1.25 = 9.463746615 Reorder the terms: 1.25 + x = 9.463746615 Solving 1.25 + x = 9.463746615 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 = 9.463746615 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 9.463746615 + -1.25 x = 9.463746615 + -1.25 Combine like terms: 9.463746615 + -1.25 = 8.213746615 x = 8.213746615 Simplifying x = 8.213746615Subproblem 2
x + 1.25 = -9.463746615 Simplifying x + 1.25 = -9.463746615 Reorder the terms: 1.25 + x = -9.463746615 Solving 1.25 + x = -9.463746615 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 = -9.463746615 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -9.463746615 + -1.25 x = -9.463746615 + -1.25 Combine like terms: -9.463746615 + -1.25 = -10.713746615 x = -10.713746615 Simplifying x = -10.713746615Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.213746615, -10.713746615}
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