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Simplifying 2x2 + 1.6x = 0.18 Reorder the terms: 1.6x + 2x2 = 0.18 Solving 1.6x + 2x2 = 0.18 Solving for variable 'x'. Reorder the terms: -0.18 + 1.6x + 2x2 = 0.18 + -0.18 Combine like terms: 0.18 + -0.18 = 0.00 -0.18 + 1.6x + 2x2 = 0.00 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.09 + 0.8x + x2 = 0.00 Move the constant term to the right: Add '0.09' to each side of the equation. -0.09 + 0.8x + 0.09 + x2 = 0.00 + 0.09 Reorder the terms: -0.09 + 0.09 + 0.8x + x2 = 0.00 + 0.09 Combine like terms: -0.09 + 0.09 = 0.00 0.00 + 0.8x + x2 = 0.00 + 0.09 0.8x + x2 = 0.00 + 0.09 Combine like terms: 0.00 + 0.09 = 0.09 0.8x + x2 = 0.09 The x term is 0.8x. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8x + 0.16 + x2 = 0.09 + 0.16 Reorder the terms: 0.16 + 0.8x + x2 = 0.09 + 0.16 Combine like terms: 0.09 + 0.16 = 0.25 0.16 + 0.8x + x2 = 0.25 Factor a perfect square on the left side: (x + 0.4)(x + 0.4) = 0.25 Calculate the square root of the right side: 0.5 Break this problem into two subproblems by setting (x + 0.4) equal to 0.5 and -0.5.Subproblem 1
x + 0.4 = 0.5 Simplifying x + 0.4 = 0.5 Reorder the terms: 0.4 + x = 0.5 Solving 0.4 + x = 0.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = 0.5 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = 0.5 + -0.4 x = 0.5 + -0.4 Combine like terms: 0.5 + -0.4 = 0.1 x = 0.1 Simplifying x = 0.1Subproblem 2
x + 0.4 = -0.5 Simplifying x + 0.4 = -0.5 Reorder the terms: 0.4 + x = -0.5 Solving 0.4 + x = -0.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = -0.5 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = -0.5 + -0.4 x = -0.5 + -0.4 Combine like terms: -0.5 + -0.4 = -0.9 x = -0.9 Simplifying x = -0.9Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1, -0.9}
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