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Simplifying x2 + -19x = 28 Reorder the terms: -19x + x2 = 28 Solving -19x + x2 = 28 Solving for variable 'x'. Reorder the terms: -28 + -19x + x2 = 28 + -28 Combine like terms: 28 + -28 = 0 -28 + -19x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '28' to each side of the equation. -28 + -19x + 28 + x2 = 0 + 28 Reorder the terms: -28 + 28 + -19x + x2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + -19x + x2 = 0 + 28 -19x + x2 = 0 + 28 Combine like terms: 0 + 28 = 28 -19x + x2 = 28 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 = 28 + 90.25 Reorder the terms: 90.25 + -19x + x2 = 28 + 90.25 Combine like terms: 28 + 90.25 = 118.25 90.25 + -19x + x2 = 118.25 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 118.25 Calculate the square root of the right side: 10.874281585 Break this problem into two subproblems by setting (x + -9.5) equal to 10.874281585 and -10.874281585.Subproblem 1
x + -9.5 = 10.874281585 Simplifying x + -9.5 = 10.874281585 Reorder the terms: -9.5 + x = 10.874281585 Solving -9.5 + x = 10.874281585 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 = 10.874281585 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 10.874281585 + 9.5 x = 10.874281585 + 9.5 Combine like terms: 10.874281585 + 9.5 = 20.374281585 x = 20.374281585 Simplifying x = 20.374281585Subproblem 2
x + -9.5 = -10.874281585 Simplifying x + -9.5 = -10.874281585 Reorder the terms: -9.5 + x = -10.874281585 Solving -9.5 + x = -10.874281585 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 = -10.874281585 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -10.874281585 + 9.5 x = -10.874281585 + 9.5 Combine like terms: -10.874281585 + 9.5 = -1.374281585 x = -1.374281585 Simplifying x = -1.374281585Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.374281585, -1.374281585}
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