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Simplifying 4x2 + -1x + -56 = 0 Reorder the terms: -56 + -1x + 4x2 = 0 Solving -56 + -1x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -14 + -0.25x + x2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + -0.25x + 14 + x2 = 0 + 14 Reorder the terms: -14 + 14 + -0.25x + x2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -0.25x + x2 = 0 + 14 -0.25x + x2 = 0 + 14 Combine like terms: 0 + 14 = 14 -0.25x + x2 = 14 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 = 14 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = 14 + 0.015625 Combine like terms: 14 + 0.015625 = 14.015625 0.015625 + -0.25x + x2 = 14.015625 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = 14.015625 Calculate the square root of the right side: 3.743744783 Break this problem into two subproblems by setting (x + -0.125) equal to 3.743744783 and -3.743744783.Subproblem 1
x + -0.125 = 3.743744783 Simplifying x + -0.125 = 3.743744783 Reorder the terms: -0.125 + x = 3.743744783 Solving -0.125 + x = 3.743744783 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 = 3.743744783 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 3.743744783 + 0.125 x = 3.743744783 + 0.125 Combine like terms: 3.743744783 + 0.125 = 3.868744783 x = 3.868744783 Simplifying x = 3.868744783Subproblem 2
x + -0.125 = -3.743744783 Simplifying x + -0.125 = -3.743744783 Reorder the terms: -0.125 + x = -3.743744783 Solving -0.125 + x = -3.743744783 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 = -3.743744783 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -3.743744783 + 0.125 x = -3.743744783 + 0.125 Combine like terms: -3.743744783 + 0.125 = -3.618744783 x = -3.618744783 Simplifying x = -3.618744783Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.868744783, -3.618744783}
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