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Simplifying 4x2 + x + -14 = 2x + -1 Reorder the terms: -14 + x + 4x2 = 2x + -1 Reorder the terms: -14 + x + 4x2 = -1 + 2x Solving -14 + x + 4x2 = -1 + 2x Solving for variable 'x'. Reorder the terms: -14 + 1 + x + -2x + 4x2 = -1 + 2x + 1 + -2x Combine like terms: -14 + 1 = -13 -13 + x + -2x + 4x2 = -1 + 2x + 1 + -2x Combine like terms: x + -2x = -1x -13 + -1x + 4x2 = -1 + 2x + 1 + -2x Reorder the terms: -13 + -1x + 4x2 = -1 + 1 + 2x + -2x Combine like terms: -1 + 1 = 0 -13 + -1x + 4x2 = 0 + 2x + -2x -13 + -1x + 4x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -13 + -1x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.25 + -0.25x + x2 = 0 Move the constant term to the right: Add '3.25' to each side of the equation. -3.25 + -0.25x + 3.25 + x2 = 0 + 3.25 Reorder the terms: -3.25 + 3.25 + -0.25x + x2 = 0 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + -0.25x + x2 = 0 + 3.25 -0.25x + x2 = 0 + 3.25 Combine like terms: 0 + 3.25 = 3.25 -0.25x + x2 = 3.25 The x term is -0.25x. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25x + 0.015625 + x2 = 3.25 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = 3.25 + 0.015625 Combine like terms: 3.25 + 0.015625 = 3.265625 0.015625 + -0.25x + x2 = 3.265625 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = 3.265625 Calculate the square root of the right side: 1.807104037 Break this problem into two subproblems by setting (x + -0.125) equal to 1.807104037 and -1.807104037.Subproblem 1
x + -0.125 = 1.807104037 Simplifying x + -0.125 = 1.807104037 Reorder the terms: -0.125 + x = 1.807104037 Solving -0.125 + x = 1.807104037 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 1.807104037 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 1.807104037 + 0.125 x = 1.807104037 + 0.125 Combine like terms: 1.807104037 + 0.125 = 1.932104037 x = 1.932104037 Simplifying x = 1.932104037Subproblem 2
x + -0.125 = -1.807104037 Simplifying x + -0.125 = -1.807104037 Reorder the terms: -0.125 + x = -1.807104037 Solving -0.125 + x = -1.807104037 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -1.807104037 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -1.807104037 + 0.125 x = -1.807104037 + 0.125 Combine like terms: -1.807104037 + 0.125 = -1.682104037 x = -1.682104037 Simplifying x = -1.682104037Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.932104037, -1.682104037}
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