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Simplifying x2 + -10x + 1 + -20 + -5x = 0 Reorder the terms: 1 + -20 + -10x + -5x + x2 = 0 Combine like terms: 1 + -20 = -19 -19 + -10x + -5x + x2 = 0 Combine like terms: -10x + -5x = -15x -19 + -15x + x2 = 0 Solving -19 + -15x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + -15x + 19 + x2 = 0 + 19 Reorder the terms: -19 + 19 + -15x + x2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -15x + x2 = 0 + 19 -15x + x2 = 0 + 19 Combine like terms: 0 + 19 = 19 -15x + x2 = 19 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 = 19 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 19 + 56.25 Combine like terms: 19 + 56.25 = 75.25 56.25 + -15x + x2 = 75.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 75.25 Calculate the square root of the right side: 8.674675786 Break this problem into two subproblems by setting (x + -7.5) equal to 8.674675786 and -8.674675786.Subproblem 1
x + -7.5 = 8.674675786 Simplifying x + -7.5 = 8.674675786 Reorder the terms: -7.5 + x = 8.674675786 Solving -7.5 + x = 8.674675786 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 = 8.674675786 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 8.674675786 + 7.5 x = 8.674675786 + 7.5 Combine like terms: 8.674675786 + 7.5 = 16.174675786 x = 16.174675786 Simplifying x = 16.174675786Subproblem 2
x + -7.5 = -8.674675786 Simplifying x + -7.5 = -8.674675786 Reorder the terms: -7.5 + x = -8.674675786 Solving -7.5 + x = -8.674675786 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 = -8.674675786 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -8.674675786 + 7.5 x = -8.674675786 + 7.5 Combine like terms: -8.674675786 + 7.5 = -1.174675786 x = -1.174675786 Simplifying x = -1.174675786Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.174675786, -1.174675786}
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