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Simplifying x2 + -21x + 2x + 42 = 0 Reorder the terms: 42 + -21x + 2x + x2 = 0 Combine like terms: -21x + 2x = -19x 42 + -19x + x2 = 0 Solving 42 + -19x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-42' to each side of the equation. 42 + -19x + -42 + x2 = 0 + -42 Reorder the terms: 42 + -42 + -19x + x2 = 0 + -42 Combine like terms: 42 + -42 = 0 0 + -19x + x2 = 0 + -42 -19x + x2 = 0 + -42 Combine like terms: 0 + -42 = -42 -19x + x2 = -42 The x term is -19x. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19x + 90.25 + x2 = -42 + 90.25 Reorder the terms: 90.25 + -19x + x2 = -42 + 90.25 Combine like terms: -42 + 90.25 = 48.25 90.25 + -19x + x2 = 48.25 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 48.25 Calculate the square root of the right side: 6.946221995 Break this problem into two subproblems by setting (x + -9.5) equal to 6.946221995 and -6.946221995.Subproblem 1
x + -9.5 = 6.946221995 Simplifying x + -9.5 = 6.946221995 Reorder the terms: -9.5 + x = 6.946221995 Solving -9.5 + x = 6.946221995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = 6.946221995 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 6.946221995 + 9.5 x = 6.946221995 + 9.5 Combine like terms: 6.946221995 + 9.5 = 16.446221995 x = 16.446221995 Simplifying x = 16.446221995Subproblem 2
x + -9.5 = -6.946221995 Simplifying x + -9.5 = -6.946221995 Reorder the terms: -9.5 + x = -6.946221995 Solving -9.5 + x = -6.946221995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = -6.946221995 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -6.946221995 + 9.5 x = -6.946221995 + 9.5 Combine like terms: -6.946221995 + 9.5 = 2.553778005 x = 2.553778005 Simplifying x = 2.553778005Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.446221995, 2.553778005}
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