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Simplifying 4x2 + 1.6x + -1 = 0 Reorder the terms: -1 + 1.6x + 4x2 = 0 Solving -1 + 1.6x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.25 + 0.4x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + 0.4x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + 0.4x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + 0.4x + x2 = 0 + 0.25 0.4x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 0.4x + x2 = 0.25 The x term is 0.4x. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4x + 0.04 + x2 = 0.25 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 0.25 + 0.04 Combine like terms: 0.25 + 0.04 = 0.29 0.04 + 0.4x + x2 = 0.29 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 0.29 Calculate the square root of the right side: 0.538516481 Break this problem into two subproblems by setting (x + 0.2) equal to 0.538516481 and -0.538516481.Subproblem 1
x + 0.2 = 0.538516481 Simplifying x + 0.2 = 0.538516481 Reorder the terms: 0.2 + x = 0.538516481 Solving 0.2 + x = 0.538516481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 0.538516481 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 0.538516481 + -0.2 x = 0.538516481 + -0.2 Combine like terms: 0.538516481 + -0.2 = 0.338516481 x = 0.338516481 Simplifying x = 0.338516481Subproblem 2
x + 0.2 = -0.538516481 Simplifying x + 0.2 = -0.538516481 Reorder the terms: 0.2 + x = -0.538516481 Solving 0.2 + x = -0.538516481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -0.538516481 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -0.538516481 + -0.2 x = -0.538516481 + -0.2 Combine like terms: -0.538516481 + -0.2 = -0.738516481 x = -0.738516481 Simplifying x = -0.738516481Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.338516481, -0.738516481}
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