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Simplifying x2 + -8 = 5x + 30 Reorder the terms: -8 + x2 = 5x + 30 Reorder the terms: -8 + x2 = 30 + 5x Solving -8 + x2 = 30 + 5x Solving for variable 'x'. Reorder the terms: -8 + -30 + -5x + x2 = 30 + 5x + -30 + -5x Combine like terms: -8 + -30 = -38 -38 + -5x + x2 = 30 + 5x + -30 + -5x Reorder the terms: -38 + -5x + x2 = 30 + -30 + 5x + -5x Combine like terms: 30 + -30 = 0 -38 + -5x + x2 = 0 + 5x + -5x -38 + -5x + x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -38 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '38' to each side of the equation. -38 + -5x + 38 + x2 = 0 + 38 Reorder the terms: -38 + 38 + -5x + x2 = 0 + 38 Combine like terms: -38 + 38 = 0 0 + -5x + x2 = 0 + 38 -5x + x2 = 0 + 38 Combine like terms: 0 + 38 = 38 -5x + x2 = 38 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 38 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 38 + 6.25 Combine like terms: 38 + 6.25 = 44.25 6.25 + -5x + x2 = 44.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 44.25 Calculate the square root of the right side: 6.652067348 Break this problem into two subproblems by setting (x + -2.5) equal to 6.652067348 and -6.652067348.Subproblem 1
x + -2.5 = 6.652067348 Simplifying x + -2.5 = 6.652067348 Reorder the terms: -2.5 + x = 6.652067348 Solving -2.5 + x = 6.652067348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 6.652067348 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 6.652067348 + 2.5 x = 6.652067348 + 2.5 Combine like terms: 6.652067348 + 2.5 = 9.152067348 x = 9.152067348 Simplifying x = 9.152067348Subproblem 2
x + -2.5 = -6.652067348 Simplifying x + -2.5 = -6.652067348 Reorder the terms: -2.5 + x = -6.652067348 Solving -2.5 + x = -6.652067348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -6.652067348 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -6.652067348 + 2.5 x = -6.652067348 + 2.5 Combine like terms: -6.652067348 + 2.5 = -4.152067348 x = -4.152067348 Simplifying x = -4.152067348Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.152067348, -4.152067348}
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