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Simplifying x2 + -33x + 42 = 0 Reorder the terms: 42 + -33x + x2 = 0 Solving 42 + -33x + 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 + -33x + -42 + x2 = 0 + -42 Reorder the terms: 42 + -42 + -33x + x2 = 0 + -42 Combine like terms: 42 + -42 = 0 0 + -33x + x2 = 0 + -42 -33x + x2 = 0 + -42 Combine like terms: 0 + -42 = -42 -33x + x2 = -42 The x term is -33x. Take half its coefficient (-16.5). Square it (272.25) and add it to both sides. Add '272.25' to each side of the equation. -33x + 272.25 + x2 = -42 + 272.25 Reorder the terms: 272.25 + -33x + x2 = -42 + 272.25 Combine like terms: -42 + 272.25 = 230.25 272.25 + -33x + x2 = 230.25 Factor a perfect square on the left side: (x + -16.5)(x + -16.5) = 230.25 Calculate the square root of the right side: 15.173990905 Break this problem into two subproblems by setting (x + -16.5) equal to 15.173990905 and -15.173990905.Subproblem 1
x + -16.5 = 15.173990905 Simplifying x + -16.5 = 15.173990905 Reorder the terms: -16.5 + x = 15.173990905 Solving -16.5 + x = 15.173990905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.5' to each side of the equation. -16.5 + 16.5 + x = 15.173990905 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + x = 15.173990905 + 16.5 x = 15.173990905 + 16.5 Combine like terms: 15.173990905 + 16.5 = 31.673990905 x = 31.673990905 Simplifying x = 31.673990905Subproblem 2
x + -16.5 = -15.173990905 Simplifying x + -16.5 = -15.173990905 Reorder the terms: -16.5 + x = -15.173990905 Solving -16.5 + x = -15.173990905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.5' to each side of the equation. -16.5 + 16.5 + x = -15.173990905 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + x = -15.173990905 + 16.5 x = -15.173990905 + 16.5 Combine like terms: -15.173990905 + 16.5 = 1.326009095 x = 1.326009095 Simplifying x = 1.326009095Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.673990905, 1.326009095}
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