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Simplifying 8x2 + 31x = 98 Reorder the terms: 31x + 8x2 = 98 Solving 31x + 8x2 = 98 Solving for variable 'x'. Reorder the terms: -98 + 31x + 8x2 = 98 + -98 Combine like terms: 98 + -98 = 0 -98 + 31x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -12.25 + 3.875x + x2 = 0 Move the constant term to the right: Add '12.25' to each side of the equation. -12.25 + 3.875x + 12.25 + x2 = 0 + 12.25 Reorder the terms: -12.25 + 12.25 + 3.875x + x2 = 0 + 12.25 Combine like terms: -12.25 + 12.25 = 0.00 0.00 + 3.875x + x2 = 0 + 12.25 3.875x + x2 = 0 + 12.25 Combine like terms: 0 + 12.25 = 12.25 3.875x + x2 = 12.25 The x term is 3.875x. Take half its coefficient (1.9375). Square it (3.75390625) and add it to both sides. Add '3.75390625' to each side of the equation. 3.875x + 3.75390625 + x2 = 12.25 + 3.75390625 Reorder the terms: 3.75390625 + 3.875x + x2 = 12.25 + 3.75390625 Combine like terms: 12.25 + 3.75390625 = 16.00390625 3.75390625 + 3.875x + x2 = 16.00390625 Factor a perfect square on the left side: (x + 1.9375)(x + 1.9375) = 16.00390625 Calculate the square root of the right side: 4.000488251 Break this problem into two subproblems by setting (x + 1.9375) equal to 4.000488251 and -4.000488251.Subproblem 1
x + 1.9375 = 4.000488251 Simplifying x + 1.9375 = 4.000488251 Reorder the terms: 1.9375 + x = 4.000488251 Solving 1.9375 + x = 4.000488251 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.9375' to each side of the equation. 1.9375 + -1.9375 + x = 4.000488251 + -1.9375 Combine like terms: 1.9375 + -1.9375 = 0.0000 0.0000 + x = 4.000488251 + -1.9375 x = 4.000488251 + -1.9375 Combine like terms: 4.000488251 + -1.9375 = 2.062988251 x = 2.062988251 Simplifying x = 2.062988251Subproblem 2
x + 1.9375 = -4.000488251 Simplifying x + 1.9375 = -4.000488251 Reorder the terms: 1.9375 + x = -4.000488251 Solving 1.9375 + x = -4.000488251 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.9375' to each side of the equation. 1.9375 + -1.9375 + x = -4.000488251 + -1.9375 Combine like terms: 1.9375 + -1.9375 = 0.0000 0.0000 + x = -4.000488251 + -1.9375 x = -4.000488251 + -1.9375 Combine like terms: -4.000488251 + -1.9375 = -5.937988251 x = -5.937988251 Simplifying x = -5.937988251Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.062988251, -5.937988251}
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