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Simplifying x2 + -19x + -56 = 0 Reorder the terms: -56 + -19x + x2 = 0 Solving -56 + -19x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '56' to each side of the equation. -56 + -19x + 56 + x2 = 0 + 56 Reorder the terms: -56 + 56 + -19x + x2 = 0 + 56 Combine like terms: -56 + 56 = 0 0 + -19x + x2 = 0 + 56 -19x + x2 = 0 + 56 Combine like terms: 0 + 56 = 56 -19x + x2 = 56 The x term is -19x. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19x + 90.25 + x2 = 56 + 90.25 Reorder the terms: 90.25 + -19x + x2 = 56 + 90.25 Combine like terms: 56 + 90.25 = 146.25 90.25 + -19x + x2 = 146.25 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 146.25 Calculate the square root of the right side: 12.093386622 Break this problem into two subproblems by setting (x + -9.5) equal to 12.093386622 and -12.093386622.Subproblem 1
x + -9.5 = 12.093386622 Simplifying x + -9.5 = 12.093386622 Reorder the terms: -9.5 + x = 12.093386622 Solving -9.5 + x = 12.093386622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = 12.093386622 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 12.093386622 + 9.5 x = 12.093386622 + 9.5 Combine like terms: 12.093386622 + 9.5 = 21.593386622 x = 21.593386622 Simplifying x = 21.593386622Subproblem 2
x + -9.5 = -12.093386622 Simplifying x + -9.5 = -12.093386622 Reorder the terms: -9.5 + x = -12.093386622 Solving -9.5 + x = -12.093386622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = -12.093386622 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -12.093386622 + 9.5 x = -12.093386622 + 9.5 Combine like terms: -12.093386622 + 9.5 = -2.593386622 x = -2.593386622 Simplifying x = -2.593386622Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.593386622, -2.593386622}
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