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Simplifying 0.2x2 + 3x + -1.8 = 0 Reorder the terms: -1.8 + 3x + 0.2x2 = 0 Solving -1.8 + 3x + 0.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. -9 + 15x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + 15x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + 15x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 15x + x2 = 0 + 9 15x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 15x + x2 = 9 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = 9 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 9 + 56.25 Combine like terms: 9 + 56.25 = 65.25 56.25 + 15x + x2 = 65.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 65.25 Calculate the square root of the right side: 8.077747211 Break this problem into two subproblems by setting (x + 7.5) equal to 8.077747211 and -8.077747211.Subproblem 1
x + 7.5 = 8.077747211 Simplifying x + 7.5 = 8.077747211 Reorder the terms: 7.5 + x = 8.077747211 Solving 7.5 + x = 8.077747211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 8.077747211 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 8.077747211 + -7.5 x = 8.077747211 + -7.5 Combine like terms: 8.077747211 + -7.5 = 0.577747211 x = 0.577747211 Simplifying x = 0.577747211Subproblem 2
x + 7.5 = -8.077747211 Simplifying x + 7.5 = -8.077747211 Reorder the terms: 7.5 + x = -8.077747211 Solving 7.5 + x = -8.077747211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -8.077747211 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -8.077747211 + -7.5 x = -8.077747211 + -7.5 Combine like terms: -8.077747211 + -7.5 = -15.577747211 x = -15.577747211 Simplifying x = -15.577747211Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.577747211, -15.577747211}
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