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Simplifying x2 + 3x + -8x + -16 = 10 Reorder the terms: -16 + 3x + -8x + x2 = 10 Combine like terms: 3x + -8x = -5x -16 + -5x + x2 = 10 Solving -16 + -5x + x2 = 10 Solving for variable 'x'. Reorder the terms: -16 + -10 + -5x + x2 = 10 + -10 Combine like terms: -16 + -10 = -26 -26 + -5x + x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -26 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '26' to each side of the equation. -26 + -5x + 26 + x2 = 0 + 26 Reorder the terms: -26 + 26 + -5x + x2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + -5x + x2 = 0 + 26 -5x + x2 = 0 + 26 Combine like terms: 0 + 26 = 26 -5x + x2 = 26 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 = 26 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 26 + 6.25 Combine like terms: 26 + 6.25 = 32.25 6.25 + -5x + x2 = 32.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 32.25 Calculate the square root of the right side: 5.678908346 Break this problem into two subproblems by setting (x + -2.5) equal to 5.678908346 and -5.678908346.Subproblem 1
x + -2.5 = 5.678908346 Simplifying x + -2.5 = 5.678908346 Reorder the terms: -2.5 + x = 5.678908346 Solving -2.5 + x = 5.678908346 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 = 5.678908346 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 5.678908346 + 2.5 x = 5.678908346 + 2.5 Combine like terms: 5.678908346 + 2.5 = 8.178908346 x = 8.178908346 Simplifying x = 8.178908346Subproblem 2
x + -2.5 = -5.678908346 Simplifying x + -2.5 = -5.678908346 Reorder the terms: -2.5 + x = -5.678908346 Solving -2.5 + x = -5.678908346 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 = -5.678908346 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -5.678908346 + 2.5 x = -5.678908346 + 2.5 Combine like terms: -5.678908346 + 2.5 = -3.178908346 x = -3.178908346 Simplifying x = -3.178908346Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.178908346, -3.178908346}
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