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Simplifying 3x + -5 = 2x2 + -14x Reorder the terms: -5 + 3x = 2x2 + -14x Reorder the terms: -5 + 3x = -14x + 2x2 Solving -5 + 3x = -14x + 2x2 Solving for variable 'x'. Combine like terms: 3x + 14x = 17x -5 + 17x + -2x2 = -14x + 2x2 + 14x + -2x2 Reorder the terms: -5 + 17x + -2x2 = -14x + 14x + 2x2 + -2x2 Combine like terms: -14x + 14x = 0 -5 + 17x + -2x2 = 0 + 2x2 + -2x2 -5 + 17x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -5 + 17x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 2.5 + -8.5x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -8.5x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -8.5x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -8.5x + x2 = 0 + -2.5 -8.5x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -8.5x + x2 = -2.5 The x term is -8.5x. Take half its coefficient (-4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. -8.5x + 18.0625 + x2 = -2.5 + 18.0625 Reorder the terms: 18.0625 + -8.5x + x2 = -2.5 + 18.0625 Combine like terms: -2.5 + 18.0625 = 15.5625 18.0625 + -8.5x + x2 = 15.5625 Factor a perfect square on the left side: (x + -4.25)(x + -4.25) = 15.5625 Calculate the square root of the right side: 3.94493346 Break this problem into two subproblems by setting (x + -4.25) equal to 3.94493346 and -3.94493346.Subproblem 1
x + -4.25 = 3.94493346 Simplifying x + -4.25 = 3.94493346 Reorder the terms: -4.25 + x = 3.94493346 Solving -4.25 + x = 3.94493346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x = 3.94493346 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = 3.94493346 + 4.25 x = 3.94493346 + 4.25 Combine like terms: 3.94493346 + 4.25 = 8.19493346 x = 8.19493346 Simplifying x = 8.19493346Subproblem 2
x + -4.25 = -3.94493346 Simplifying x + -4.25 = -3.94493346 Reorder the terms: -4.25 + x = -3.94493346 Solving -4.25 + x = -3.94493346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x = -3.94493346 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = -3.94493346 + 4.25 x = -3.94493346 + 4.25 Combine like terms: -3.94493346 + 4.25 = 0.30506654 x = 0.30506654 Simplifying x = 0.30506654Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.19493346, 0.30506654}
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