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Simplifying 3.14x2 + 12.56x + -131.35 = 0 Reorder the terms: -131.35 + 12.56x + 3.14x2 = 0 Solving -131.35 + 12.56x + 3.14x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3.14 the coefficient of the squared term: Divide each side by '3.14'. -41.83121019 + 4x + x2 = 0 Move the constant term to the right: Add '41.83121019' to each side of the equation. -41.83121019 + 4x + 41.83121019 + x2 = 0 + 41.83121019 Reorder the terms: -41.83121019 + 41.83121019 + 4x + x2 = 0 + 41.83121019 Combine like terms: -41.83121019 + 41.83121019 = 0.00000000 0.00000000 + 4x + x2 = 0 + 41.83121019 4x + x2 = 0 + 41.83121019 Combine like terms: 0 + 41.83121019 = 41.83121019 4x + x2 = 41.83121019 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 41.83121019 + 4 Reorder the terms: 4 + 4x + x2 = 41.83121019 + 4 Combine like terms: 41.83121019 + 4 = 45.83121019 4 + 4x + x2 = 45.83121019 Factor a perfect square on the left side: (x + 2)(x + 2) = 45.83121019 Calculate the square root of the right side: 6.769875198 Break this problem into two subproblems by setting (x + 2) equal to 6.769875198 and -6.769875198.Subproblem 1
x + 2 = 6.769875198 Simplifying x + 2 = 6.769875198 Reorder the terms: 2 + x = 6.769875198 Solving 2 + x = 6.769875198 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 6.769875198 + -2 Combine like terms: 2 + -2 = 0 0 + x = 6.769875198 + -2 x = 6.769875198 + -2 Combine like terms: 6.769875198 + -2 = 4.769875198 x = 4.769875198 Simplifying x = 4.769875198Subproblem 2
x + 2 = -6.769875198 Simplifying x + 2 = -6.769875198 Reorder the terms: 2 + x = -6.769875198 Solving 2 + x = -6.769875198 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -6.769875198 + -2 Combine like terms: 2 + -2 = 0 0 + x = -6.769875198 + -2 x = -6.769875198 + -2 Combine like terms: -6.769875198 + -2 = -8.769875198 x = -8.769875198 Simplifying x = -8.769875198Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.769875198, -8.769875198}
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