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Simplifying 2x2 + 12x + -31 = 0 Reorder the terms: -31 + 12x + 2x2 = 0 Solving -31 + 12x + 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'. -15.5 + 6x + x2 = 0 Move the constant term to the right: Add '15.5' to each side of the equation. -15.5 + 6x + 15.5 + x2 = 0 + 15.5 Reorder the terms: -15.5 + 15.5 + 6x + x2 = 0 + 15.5 Combine like terms: -15.5 + 15.5 = 0.0 0.0 + 6x + x2 = 0 + 15.5 6x + x2 = 0 + 15.5 Combine like terms: 0 + 15.5 = 15.5 6x + x2 = 15.5 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 15.5 + 9 Reorder the terms: 9 + 6x + x2 = 15.5 + 9 Combine like terms: 15.5 + 9 = 24.5 9 + 6x + x2 = 24.5 Factor a perfect square on the left side: (x + 3)(x + 3) = 24.5 Calculate the square root of the right side: 4.949747468 Break this problem into two subproblems by setting (x + 3) equal to 4.949747468 and -4.949747468.Subproblem 1
x + 3 = 4.949747468 Simplifying x + 3 = 4.949747468 Reorder the terms: 3 + x = 4.949747468 Solving 3 + x = 4.949747468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 4.949747468 + -3 Combine like terms: 3 + -3 = 0 0 + x = 4.949747468 + -3 x = 4.949747468 + -3 Combine like terms: 4.949747468 + -3 = 1.949747468 x = 1.949747468 Simplifying x = 1.949747468Subproblem 2
x + 3 = -4.949747468 Simplifying x + 3 = -4.949747468 Reorder the terms: 3 + x = -4.949747468 Solving 3 + x = -4.949747468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -4.949747468 + -3 Combine like terms: 3 + -3 = 0 0 + x = -4.949747468 + -3 x = -4.949747468 + -3 Combine like terms: -4.949747468 + -3 = -7.949747468 x = -7.949747468 Simplifying x = -7.949747468Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.949747468, -7.949747468}
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