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Simplifying 3x2 + -18x + 0.03 = 0 Reorder the terms: 0.03 + -18x + 3x2 = 0 Solving 0.03 + -18x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.01 + -6x + x2 = 0 Move the constant term to the right: Add '-0.01' to each side of the equation. 0.01 + -6x + -0.01 + x2 = 0 + -0.01 Reorder the terms: 0.01 + -0.01 + -6x + x2 = 0 + -0.01 Combine like terms: 0.01 + -0.01 = 0.00 0.00 + -6x + x2 = 0 + -0.01 -6x + x2 = 0 + -0.01 Combine like terms: 0 + -0.01 = -0.01 -6x + x2 = -0.01 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -0.01 + 9 Reorder the terms: 9 + -6x + x2 = -0.01 + 9 Combine like terms: -0.01 + 9 = 8.99 9 + -6x + x2 = 8.99 Factor a perfect square on the left side: (x + -3)(x + -3) = 8.99 Calculate the square root of the right side: 2.99833287 Break this problem into two subproblems by setting (x + -3) equal to 2.99833287 and -2.99833287.Subproblem 1
x + -3 = 2.99833287 Simplifying x + -3 = 2.99833287 Reorder the terms: -3 + x = 2.99833287 Solving -3 + x = 2.99833287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 2.99833287 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.99833287 + 3 x = 2.99833287 + 3 Combine like terms: 2.99833287 + 3 = 5.99833287 x = 5.99833287 Simplifying x = 5.99833287Subproblem 2
x + -3 = -2.99833287 Simplifying x + -3 = -2.99833287 Reorder the terms: -3 + x = -2.99833287 Solving -3 + x = -2.99833287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -2.99833287 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.99833287 + 3 x = -2.99833287 + 3 Combine like terms: -2.99833287 + 3 = 0.00166713 x = 0.00166713 Simplifying x = 0.00166713Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.99833287, 0.00166713}
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