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Simplifying 4x2(1 + -1x2) = 0.1 (1 * 4x2 + -1x2 * 4x2) = 0.1 (4x2 + -4x4) = 0.1 Solving 4x2 + -4x4 = 0.1 Solving for variable 'x'. Reorder the terms: -0.1 + 4x2 + -4x4 = 0.1 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 -0.1 + 4x2 + -4x4 = 0.0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 0.025 + -1x2 + x4 = 0.0 Move the constant term to the right: Add '-0.025' to each side of the equation. 0.025 + -1x2 + -0.025 + x4 = 0.0 + -0.025 Reorder the terms: 0.025 + -0.025 + -1x2 + x4 = 0.0 + -0.025 Combine like terms: 0.025 + -0.025 = 0.000 0.000 + -1x2 + x4 = 0.0 + -0.025 -1x2 + x4 = 0.0 + -0.025 Combine like terms: 0.0 + -0.025 = -0.025 -1x2 + x4 = -0.025 The x term is -1x2. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x2 + 0.25 + x4 = -0.025 + 0.25 Reorder the terms: 0.25 + -1x2 + x4 = -0.025 + 0.25 Combine like terms: -0.025 + 0.25 = 0.225 0.25 + -1x2 + x4 = 0.225 Factor a perfect square on the left side: (x2 + -0.5)(x2 + -0.5) = 0.225 Calculate the square root of the right side: 0.474341649 Break this problem into two subproblems by setting (x2 + -0.5) equal to 0.474341649 and -0.474341649.Subproblem 1
x2 + -0.5 = 0.474341649 Simplifying x2 + -0.5 = 0.474341649 Reorder the terms: -0.5 + x2 = 0.474341649 Solving -0.5 + x2 = 0.474341649 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x2 = 0.474341649 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x2 = 0.474341649 + 0.5 x2 = 0.474341649 + 0.5 Combine like terms: 0.474341649 + 0.5 = 0.974341649 x2 = 0.974341649 Simplifying x2 = 0.974341649 Take the square root of each side: x = {-0.987087458, 0.987087458}Subproblem 2
x2 + -0.5 = -0.474341649 Simplifying x2 + -0.5 = -0.474341649 Reorder the terms: -0.5 + x2 = -0.474341649 Solving -0.5 + x2 = -0.474341649 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x2 = -0.474341649 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x2 = -0.474341649 + 0.5 x2 = -0.474341649 + 0.5 Combine like terms: -0.474341649 + 0.5 = 0.025658351 x2 = 0.025658351 Simplifying x2 = 0.025658351 Take the square root of each side: x = {-0.160182243, 0.160182243}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.987087458, 0.987087458, -0.160182243, 0.160182243}
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