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Simplifying 0.015x2 + -0.12x + 0.20 = 0 Reorder the terms: 0.20 + -0.12x + 0.015x2 = 0 Solving 0.20 + -0.12x + 0.015x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.015 the coefficient of the squared term: Divide each side by '0.015'. 13.33333333 + -8x + x2 = 0 Move the constant term to the right: Add '-13.33333333' to each side of the equation. 13.33333333 + -8x + -13.33333333 + x2 = 0 + -13.33333333 Reorder the terms: 13.33333333 + -13.33333333 + -8x + x2 = 0 + -13.33333333 Combine like terms: 13.33333333 + -13.33333333 = 0.00000000 0.00000000 + -8x + x2 = 0 + -13.33333333 -8x + x2 = 0 + -13.33333333 Combine like terms: 0 + -13.33333333 = -13.33333333 -8x + x2 = -13.33333333 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -13.33333333 + 16 Reorder the terms: 16 + -8x + x2 = -13.33333333 + 16 Combine like terms: -13.33333333 + 16 = 2.66666667 16 + -8x + x2 = 2.66666667 Factor a perfect square on the left side: (x + -4)(x + -4) = 2.66666667 Calculate the square root of the right side: 1.632993163 Break this problem into two subproblems by setting (x + -4) equal to 1.632993163 and -1.632993163.Subproblem 1
x + -4 = 1.632993163 Simplifying x + -4 = 1.632993163 Reorder the terms: -4 + x = 1.632993163 Solving -4 + x = 1.632993163 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 1.632993163 + 4 Combine like terms: -4 + 4 = 0 0 + x = 1.632993163 + 4 x = 1.632993163 + 4 Combine like terms: 1.632993163 + 4 = 5.632993163 x = 5.632993163 Simplifying x = 5.632993163Subproblem 2
x + -4 = -1.632993163 Simplifying x + -4 = -1.632993163 Reorder the terms: -4 + x = -1.632993163 Solving -4 + x = -1.632993163 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -1.632993163 + 4 Combine like terms: -4 + 4 = 0 0 + x = -1.632993163 + 4 x = -1.632993163 + 4 Combine like terms: -1.632993163 + 4 = 2.367006837 x = 2.367006837 Simplifying x = 2.367006837Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.632993163, 2.367006837}
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