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Simplifying 0 = 0.2x2 + 3x + -20 Reorder the terms: 0 = -20 + 3x + 0.2x2 Solving 0 = -20 + 3x + 0.2x2 Solving for variable 'x'. Combine like terms: 0 + 20 = 20 20 + -3x + -0.2x2 = -20 + 3x + 0.2x2 + 20 + -3x + -0.2x2 Reorder the terms: 20 + -3x + -0.2x2 = -20 + 20 + 3x + -3x + 0.2x2 + -0.2x2 Combine like terms: -20 + 20 = 0 20 + -3x + -0.2x2 = 0 + 3x + -3x + 0.2x2 + -0.2x2 20 + -3x + -0.2x2 = 3x + -3x + 0.2x2 + -0.2x2 Combine like terms: 3x + -3x = 0 20 + -3x + -0.2x2 = 0 + 0.2x2 + -0.2x2 20 + -3x + -0.2x2 = 0.2x2 + -0.2x2 Combine like terms: 0.2x2 + -0.2x2 = 0.0 20 + -3x + -0.2x2 = 0.0 Begin completing the square. Divide all terms by -0.2 the coefficient of the squared term: Divide each side by '-0.2'. -100 + 15x + x2 = 0 Move the constant term to the right: Add '100' to each side of the equation. -100 + 15x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + 15x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 15x + x2 = 0 + 100 15x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 15x + x2 = 100 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 = 100 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 100 + 56.25 Combine like terms: 100 + 56.25 = 156.25 56.25 + 15x + x2 = 156.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 156.25 Calculate the square root of the right side: 12.5 Break this problem into two subproblems by setting (x + 7.5) equal to 12.5 and -12.5.Subproblem 1
x + 7.5 = 12.5 Simplifying x + 7.5 = 12.5 Reorder the terms: 7.5 + x = 12.5 Solving 7.5 + x = 12.5 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 = 12.5 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 12.5 + -7.5 x = 12.5 + -7.5 Combine like terms: 12.5 + -7.5 = 5 x = 5 Simplifying x = 5Subproblem 2
x + 7.5 = -12.5 Simplifying x + 7.5 = -12.5 Reorder the terms: 7.5 + x = -12.5 Solving 7.5 + x = -12.5 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 = -12.5 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -12.5 + -7.5 x = -12.5 + -7.5 Combine like terms: -12.5 + -7.5 = -20 x = -20 Simplifying x = -20Solution
The solution to the problem is based on the solutions from the subproblems. x = {5, -20}
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