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Simplifying 10x2 + -33x + 18 = 0 Reorder the terms: 18 + -33x + 10x2 = 0 Solving 18 + -33x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 1.8 + -3.3x + x2 = 0 Move the constant term to the right: Add '-1.8' to each side of the equation. 1.8 + -3.3x + -1.8 + x2 = 0 + -1.8 Reorder the terms: 1.8 + -1.8 + -3.3x + x2 = 0 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + -3.3x + x2 = 0 + -1.8 -3.3x + x2 = 0 + -1.8 Combine like terms: 0 + -1.8 = -1.8 -3.3x + x2 = -1.8 The x term is -3.3x. Take half its coefficient (-1.65). Square it (2.7225) and add it to both sides. Add '2.7225' to each side of the equation. -3.3x + 2.7225 + x2 = -1.8 + 2.7225 Reorder the terms: 2.7225 + -3.3x + x2 = -1.8 + 2.7225 Combine like terms: -1.8 + 2.7225 = 0.9225 2.7225 + -3.3x + x2 = 0.9225 Factor a perfect square on the left side: (x + -1.65)(x + -1.65) = 0.9225 Calculate the square root of the right side: 0.960468636 Break this problem into two subproblems by setting (x + -1.65) equal to 0.960468636 and -0.960468636.Subproblem 1
x + -1.65 = 0.960468636 Simplifying x + -1.65 = 0.960468636 Reorder the terms: -1.65 + x = 0.960468636 Solving -1.65 + x = 0.960468636 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.65' to each side of the equation. -1.65 + 1.65 + x = 0.960468636 + 1.65 Combine like terms: -1.65 + 1.65 = 0.00 0.00 + x = 0.960468636 + 1.65 x = 0.960468636 + 1.65 Combine like terms: 0.960468636 + 1.65 = 2.610468636 x = 2.610468636 Simplifying x = 2.610468636Subproblem 2
x + -1.65 = -0.960468636 Simplifying x + -1.65 = -0.960468636 Reorder the terms: -1.65 + x = -0.960468636 Solving -1.65 + x = -0.960468636 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.65' to each side of the equation. -1.65 + 1.65 + x = -0.960468636 + 1.65 Combine like terms: -1.65 + 1.65 = 0.00 0.00 + x = -0.960468636 + 1.65 x = -0.960468636 + 1.65 Combine like terms: -0.960468636 + 1.65 = 0.689531364 x = 0.689531364 Simplifying x = 0.689531364Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.610468636, 0.689531364}
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