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Simplifying 0.2x2 + 0.1x = 0.5625 Reorder the terms: 0.1x + 0.2x2 = 0.5625 Solving 0.1x + 0.2x2 = 0.5625 Solving for variable 'x'. Reorder the terms: -0.5625 + 0.1x + 0.2x2 = 0.5625 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 -0.5625 + 0.1x + 0.2x2 = 0.0000 Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. -2.8125 + 0.5x + x2 = 0.000 Move the constant term to the right: Add '2.8125' to each side of the equation. -2.8125 + 0.5x + 2.8125 + x2 = 0.000 + 2.8125 Reorder the terms: -2.8125 + 2.8125 + 0.5x + x2 = 0.000 + 2.8125 Combine like terms: -2.8125 + 2.8125 = 0.0000 0.0000 + 0.5x + x2 = 0.000 + 2.8125 0.5x + x2 = 0.000 + 2.8125 Combine like terms: 0.000 + 2.8125 = 2.8125 0.5x + x2 = 2.8125 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 2.8125 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 2.8125 + 0.0625 Combine like terms: 2.8125 + 0.0625 = 2.875 0.0625 + 0.5x + x2 = 2.875 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 2.875 Calculate the square root of the right side: 1.695582496 Break this problem into two subproblems by setting (x + 0.25) equal to 1.695582496 and -1.695582496.Subproblem 1
x + 0.25 = 1.695582496 Simplifying x + 0.25 = 1.695582496 Reorder the terms: 0.25 + x = 1.695582496 Solving 0.25 + x = 1.695582496 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 1.695582496 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 1.695582496 + -0.25 x = 1.695582496 + -0.25 Combine like terms: 1.695582496 + -0.25 = 1.445582496 x = 1.445582496 Simplifying x = 1.445582496Subproblem 2
x + 0.25 = -1.695582496 Simplifying x + 0.25 = -1.695582496 Reorder the terms: 0.25 + x = -1.695582496 Solving 0.25 + x = -1.695582496 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -1.695582496 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -1.695582496 + -0.25 x = -1.695582496 + -0.25 Combine like terms: -1.695582496 + -0.25 = -1.945582496 x = -1.945582496 Simplifying x = -1.945582496Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.445582496, -1.945582496}
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