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Simplifying 0.2x2 + -0.9x + 1 = 0 Reorder the terms: 1 + -0.9x + 0.2x2 = 0 Solving 1 + -0.9x + 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'. 5 + -4.5x + x2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + -4.5x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -4.5x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4.5x + x2 = 0 + -5 -4.5x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -4.5x + x2 = -5 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = -5 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = -5 + 5.0625 Combine like terms: -5 + 5.0625 = 0.0625 5.0625 + -4.5x + x2 = 0.0625 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 0.0625 Calculate the square root of the right side: 0.25 Break this problem into two subproblems by setting (x + -2.25) equal to 0.25 and -0.25.Subproblem 1
x + -2.25 = 0.25 Simplifying x + -2.25 = 0.25 Reorder the terms: -2.25 + x = 0.25 Solving -2.25 + x = 0.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 0.25 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 0.25 + 2.25 x = 0.25 + 2.25 Combine like terms: 0.25 + 2.25 = 2.5 x = 2.5 Simplifying x = 2.5Subproblem 2
x + -2.25 = -0.25 Simplifying x + -2.25 = -0.25 Reorder the terms: -2.25 + x = -0.25 Solving -2.25 + x = -0.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -0.25 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -0.25 + 2.25 x = -0.25 + 2.25 Combine like terms: -0.25 + 2.25 = 2 x = 2 Simplifying x = 2Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.5, 2}
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