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Simplifying x2 + -13x = -21 Reorder the terms: -13x + x2 = -21 Solving -13x + x2 = -21 Solving for variable 'x'. Reorder the terms: 21 + -13x + x2 = -21 + 21 Combine like terms: -21 + 21 = 0 21 + -13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-21' to each side of the equation. 21 + -13x + -21 + x2 = 0 + -21 Reorder the terms: 21 + -21 + -13x + x2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + -13x + x2 = 0 + -21 -13x + x2 = 0 + -21 Combine like terms: 0 + -21 = -21 -13x + x2 = -21 The x term is -13x. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13x + 42.25 + x2 = -21 + 42.25 Reorder the terms: 42.25 + -13x + x2 = -21 + 42.25 Combine like terms: -21 + 42.25 = 21.25 42.25 + -13x + x2 = 21.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 21.25 Calculate the square root of the right side: 4.609772229 Break this problem into two subproblems by setting (x + -6.5) equal to 4.609772229 and -4.609772229.Subproblem 1
x + -6.5 = 4.609772229 Simplifying x + -6.5 = 4.609772229 Reorder the terms: -6.5 + x = 4.609772229 Solving -6.5 + x = 4.609772229 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = 4.609772229 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 4.609772229 + 6.5 x = 4.609772229 + 6.5 Combine like terms: 4.609772229 + 6.5 = 11.109772229 x = 11.109772229 Simplifying x = 11.109772229Subproblem 2
x + -6.5 = -4.609772229 Simplifying x + -6.5 = -4.609772229 Reorder the terms: -6.5 + x = -4.609772229 Solving -6.5 + x = -4.609772229 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = -4.609772229 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -4.609772229 + 6.5 x = -4.609772229 + 6.5 Combine like terms: -4.609772229 + 6.5 = 1.890227771 x = 1.890227771 Simplifying x = 1.890227771Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.109772229, 1.890227771}
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