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Simplifying -8x2 + -119x + 312 = 0 Reorder the terms: 312 + -119x + -8x2 = 0 Solving 312 + -119x + -8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -39 + 14.875x + x2 = 0 Move the constant term to the right: Add '39' to each side of the equation. -39 + 14.875x + 39 + x2 = 0 + 39 Reorder the terms: -39 + 39 + 14.875x + x2 = 0 + 39 Combine like terms: -39 + 39 = 0 0 + 14.875x + x2 = 0 + 39 14.875x + x2 = 0 + 39 Combine like terms: 0 + 39 = 39 14.875x + x2 = 39 The x term is 14.875x. Take half its coefficient (7.4375). Square it (55.31640625) and add it to both sides. Add '55.31640625' to each side of the equation. 14.875x + 55.31640625 + x2 = 39 + 55.31640625 Reorder the terms: 55.31640625 + 14.875x + x2 = 39 + 55.31640625 Combine like terms: 39 + 55.31640625 = 94.31640625 55.31640625 + 14.875x + x2 = 94.31640625 Factor a perfect square on the left side: (x + 7.4375)(x + 7.4375) = 94.31640625 Calculate the square root of the right side: 9.711663413 Break this problem into two subproblems by setting (x + 7.4375) equal to 9.711663413 and -9.711663413.Subproblem 1
x + 7.4375 = 9.711663413 Simplifying x + 7.4375 = 9.711663413 Reorder the terms: 7.4375 + x = 9.711663413 Solving 7.4375 + x = 9.711663413 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.4375' to each side of the equation. 7.4375 + -7.4375 + x = 9.711663413 + -7.4375 Combine like terms: 7.4375 + -7.4375 = 0.0000 0.0000 + x = 9.711663413 + -7.4375 x = 9.711663413 + -7.4375 Combine like terms: 9.711663413 + -7.4375 = 2.274163413 x = 2.274163413 Simplifying x = 2.274163413Subproblem 2
x + 7.4375 = -9.711663413 Simplifying x + 7.4375 = -9.711663413 Reorder the terms: 7.4375 + x = -9.711663413 Solving 7.4375 + x = -9.711663413 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.4375' to each side of the equation. 7.4375 + -7.4375 + x = -9.711663413 + -7.4375 Combine like terms: 7.4375 + -7.4375 = 0.0000 0.0000 + x = -9.711663413 + -7.4375 x = -9.711663413 + -7.4375 Combine like terms: -9.711663413 + -7.4375 = -17.149163413 x = -17.149163413 Simplifying x = -17.149163413Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.274163413, -17.149163413}
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