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Simplifying x2 = -5x + 26 Reorder the terms: x2 = 26 + -5x Solving x2 = 26 + -5x Solving for variable 'x'. Reorder the terms: -26 + 5x + x2 = 26 + -5x + -26 + 5x Reorder the terms: -26 + 5x + x2 = 26 + -26 + -5x + 5x Combine like terms: 26 + -26 = 0 -26 + 5x + x2 = 0 + -5x + 5x -26 + 5x + x2 = -5x + 5x Combine like terms: -5x + 5x = 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 = 3.178908346 x = 3.178908346 Simplifying x = 3.178908346Subproblem 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 = -8.178908346 x = -8.178908346 Simplifying x = -8.178908346Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.178908346, -8.178908346}
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