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Simplifying 2x2 + 31x + -5.7 = 0 Reorder the terms: -5.7 + 31x + 2x2 = 0 Solving -5.7 + 31x + 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'. -2.85 + 15.5x + x2 = 0 Move the constant term to the right: Add '2.85' to each side of the equation. -2.85 + 15.5x + 2.85 + x2 = 0 + 2.85 Reorder the terms: -2.85 + 2.85 + 15.5x + x2 = 0 + 2.85 Combine like terms: -2.85 + 2.85 = 0.00 0.00 + 15.5x + x2 = 0 + 2.85 15.5x + x2 = 0 + 2.85 Combine like terms: 0 + 2.85 = 2.85 15.5x + x2 = 2.85 The x term is 15.5x. Take half its coefficient (7.75). Square it (60.0625) and add it to both sides. Add '60.0625' to each side of the equation. 15.5x + 60.0625 + x2 = 2.85 + 60.0625 Reorder the terms: 60.0625 + 15.5x + x2 = 2.85 + 60.0625 Combine like terms: 2.85 + 60.0625 = 62.9125 60.0625 + 15.5x + x2 = 62.9125 Factor a perfect square on the left side: (x + 7.75)(x + 7.75) = 62.9125 Calculate the square root of the right side: 7.931740036 Break this problem into two subproblems by setting (x + 7.75) equal to 7.931740036 and -7.931740036.Subproblem 1
x + 7.75 = 7.931740036 Simplifying x + 7.75 = 7.931740036 Reorder the terms: 7.75 + x = 7.931740036 Solving 7.75 + x = 7.931740036 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.75' to each side of the equation. 7.75 + -7.75 + x = 7.931740036 + -7.75 Combine like terms: 7.75 + -7.75 = 0.00 0.00 + x = 7.931740036 + -7.75 x = 7.931740036 + -7.75 Combine like terms: 7.931740036 + -7.75 = 0.181740036 x = 0.181740036 Simplifying x = 0.181740036Subproblem 2
x + 7.75 = -7.931740036 Simplifying x + 7.75 = -7.931740036 Reorder the terms: 7.75 + x = -7.931740036 Solving 7.75 + x = -7.931740036 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.75' to each side of the equation. 7.75 + -7.75 + x = -7.931740036 + -7.75 Combine like terms: 7.75 + -7.75 = 0.00 0.00 + x = -7.931740036 + -7.75 x = -7.931740036 + -7.75 Combine like terms: -7.931740036 + -7.75 = -15.681740036 x = -15.681740036 Simplifying x = -15.681740036Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.181740036, -15.681740036}
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