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Simplifying 31 = (x + 3.5)(x) Reorder the terms: 31 = (3.5 + x)(x) Reorder the terms for easier multiplication: 31 = x(3.5 + x) 31 = (3.5 * x + x * x) 31 = (3.5x + x2) Solving 31 = 3.5x + x2 Solving for variable 'x'. Reorder the terms: 31 + -3.5x + -1x2 = 3.5x + -3.5x + x2 + -1x2 Combine like terms: 3.5x + -3.5x = 0.0 31 + -3.5x + -1x2 = 0.0 + x2 + -1x2 31 + -3.5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 31 + -3.5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -31 + 3.5x + x2 = 0 Move the constant term to the right: Add '31' to each side of the equation. -31 + 3.5x + 31 + x2 = 0 + 31 Reorder the terms: -31 + 31 + 3.5x + x2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + 3.5x + x2 = 0 + 31 3.5x + x2 = 0 + 31 Combine like terms: 0 + 31 = 31 3.5x + x2 = 31 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 31 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 31 + 3.0625 Combine like terms: 31 + 3.0625 = 34.0625 3.0625 + 3.5x + x2 = 34.0625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 34.0625 Calculate the square root of the right side: 5.836308765 Break this problem into two subproblems by setting (x + 1.75) equal to 5.836308765 and -5.836308765.Subproblem 1
x + 1.75 = 5.836308765 Simplifying x + 1.75 = 5.836308765 Reorder the terms: 1.75 + x = 5.836308765 Solving 1.75 + x = 5.836308765 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 5.836308765 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 5.836308765 + -1.75 x = 5.836308765 + -1.75 Combine like terms: 5.836308765 + -1.75 = 4.086308765 x = 4.086308765 Simplifying x = 4.086308765Subproblem 2
x + 1.75 = -5.836308765 Simplifying x + 1.75 = -5.836308765 Reorder the terms: 1.75 + x = -5.836308765 Solving 1.75 + x = -5.836308765 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -5.836308765 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -5.836308765 + -1.75 x = -5.836308765 + -1.75 Combine like terms: -5.836308765 + -1.75 = -7.586308765 x = -7.586308765 Simplifying x = -7.586308765Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.086308765, -7.586308765}
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