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Simplifying 0.2x2 + -0.3x + -0.5 = 0 Reorder the terms: -0.5 + -0.3x + 0.2x2 = 0 Solving -0.5 + -0.3x + 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'. -2.5 + -1.5x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -1.5x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -1.5x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -1.5x + x2 = 0 + 2.5 -1.5x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -1.5x + x2 = 2.5 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 2.5 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 2.5 + 0.5625 Combine like terms: 2.5 + 0.5625 = 3.0625 0.5625 + -1.5x + x2 = 3.0625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 3.0625 Calculate the square root of the right side: 1.75 Break this problem into two subproblems by setting (x + -0.75) equal to 1.75 and -1.75.Subproblem 1
x + -0.75 = 1.75 Simplifying x + -0.75 = 1.75 Reorder the terms: -0.75 + x = 1.75 Solving -0.75 + x = 1.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 1.75 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 1.75 + 0.75 x = 1.75 + 0.75 Combine like terms: 1.75 + 0.75 = 2.5 x = 2.5 Simplifying x = 2.5Subproblem 2
x + -0.75 = -1.75 Simplifying x + -0.75 = -1.75 Reorder the terms: -0.75 + x = -1.75 Solving -0.75 + x = -1.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -1.75 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -1.75 + 0.75 x = -1.75 + 0.75 Combine like terms: -1.75 + 0.75 = -1 x = -1 Simplifying x = -1Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.5, -1}
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