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Simplifying x2 + 20x = 33 Reorder the terms: 20x + x2 = 33 Solving 20x + x2 = 33 Solving for variable 'x'. Reorder the terms: -33 + 20x + x2 = 33 + -33 Combine like terms: 33 + -33 = 0 -33 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '33' to each side of the equation. -33 + 20x + 33 + x2 = 0 + 33 Reorder the terms: -33 + 33 + 20x + x2 = 0 + 33 Combine like terms: -33 + 33 = 0 0 + 20x + x2 = 0 + 33 20x + x2 = 0 + 33 Combine like terms: 0 + 33 = 33 20x + x2 = 33 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 33 + 100 Reorder the terms: 100 + 20x + x2 = 33 + 100 Combine like terms: 33 + 100 = 133 100 + 20x + x2 = 133 Factor a perfect square on the left side: (x + 10)(x + 10) = 133 Calculate the square root of the right side: 11.532562595 Break this problem into two subproblems by setting (x + 10) equal to 11.532562595 and -11.532562595.Subproblem 1
x + 10 = 11.532562595 Simplifying x + 10 = 11.532562595 Reorder the terms: 10 + x = 11.532562595 Solving 10 + x = 11.532562595 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 11.532562595 + -10 Combine like terms: 10 + -10 = 0 0 + x = 11.532562595 + -10 x = 11.532562595 + -10 Combine like terms: 11.532562595 + -10 = 1.532562595 x = 1.532562595 Simplifying x = 1.532562595Subproblem 2
x + 10 = -11.532562595 Simplifying x + 10 = -11.532562595 Reorder the terms: 10 + x = -11.532562595 Solving 10 + x = -11.532562595 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -11.532562595 + -10 Combine like terms: 10 + -10 = 0 0 + x = -11.532562595 + -10 x = -11.532562595 + -10 Combine like terms: -11.532562595 + -10 = -21.532562595 x = -21.532562595 Simplifying x = -21.532562595Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.532562595, -21.532562595}
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