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Simplifying x2 + -15x + 35 = 0 Reorder the terms: 35 + -15x + x2 = 0 Solving 35 + -15x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-35' to each side of the equation. 35 + -15x + -35 + x2 = 0 + -35 Reorder the terms: 35 + -35 + -15x + x2 = 0 + -35 Combine like terms: 35 + -35 = 0 0 + -15x + x2 = 0 + -35 -15x + x2 = 0 + -35 Combine like terms: 0 + -35 = -35 -15x + x2 = -35 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = -35 + 56.25 Reorder the terms: 56.25 + -15x + x2 = -35 + 56.25 Combine like terms: -35 + 56.25 = 21.25 56.25 + -15x + x2 = 21.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 21.25 Calculate the square root of the right side: 4.609772229 Break this problem into two subproblems by setting (x + -7.5) equal to 4.609772229 and -4.609772229.Subproblem 1
x + -7.5 = 4.609772229 Simplifying x + -7.5 = 4.609772229 Reorder the terms: -7.5 + x = 4.609772229 Solving -7.5 + x = 4.609772229 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 4.609772229 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 4.609772229 + 7.5 x = 4.609772229 + 7.5 Combine like terms: 4.609772229 + 7.5 = 12.109772229 x = 12.109772229 Simplifying x = 12.109772229Subproblem 2
x + -7.5 = -4.609772229 Simplifying x + -7.5 = -4.609772229 Reorder the terms: -7.5 + x = -4.609772229 Solving -7.5 + x = -4.609772229 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -4.609772229 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -4.609772229 + 7.5 x = -4.609772229 + 7.5 Combine like terms: -4.609772229 + 7.5 = 2.890227771 x = 2.890227771 Simplifying x = 2.890227771Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.109772229, 2.890227771}
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