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Simplifying 2x2 + -1x4 = 0.99 Solving 2x2 + -1x4 = 0.99 Solving for variable 'x'. Reorder the terms: -0.99 + 2x2 + -1x4 = 0.99 + -0.99 Combine like terms: 0.99 + -0.99 = 0.00 -0.99 + 2x2 + -1x4 = 0.00 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 0.99 + -2x2 + x4 = 0.00 Move the constant term to the right: Add '-0.99' to each side of the equation. 0.99 + -2x2 + -0.99 + x4 = 0.00 + -0.99 Reorder the terms: 0.99 + -0.99 + -2x2 + x4 = 0.00 + -0.99 Combine like terms: 0.99 + -0.99 = 0.00 0.00 + -2x2 + x4 = 0.00 + -0.99 -2x2 + x4 = 0.00 + -0.99 Combine like terms: 0.00 + -0.99 = -0.99 -2x2 + x4 = -0.99 The x term is -2x2. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x2 + 1 + x4 = -0.99 + 1 Reorder the terms: 1 + -2x2 + x4 = -0.99 + 1 Combine like terms: -0.99 + 1 = 0.01 1 + -2x2 + x4 = 0.01 Factor a perfect square on the left side: (x2 + -1)(x2 + -1) = 0.01 Calculate the square root of the right side: 0.1 Break this problem into two subproblems by setting (x2 + -1) equal to 0.1 and -0.1.Subproblem 1
x2 + -1 = 0.1 Simplifying x2 + -1 = 0.1 Reorder the terms: -1 + x2 = 0.1 Solving -1 + x2 = 0.1 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x2 = 0.1 + 1 Combine like terms: -1 + 1 = 0 0 + x2 = 0.1 + 1 x2 = 0.1 + 1 Combine like terms: 0.1 + 1 = 1.1 x2 = 1.1 Simplifying x2 = 1.1 Take the square root of each side: x = {-1.048808848, 1.048808848}Subproblem 2
x2 + -1 = -0.1 Simplifying x2 + -1 = -0.1 Reorder the terms: -1 + x2 = -0.1 Solving -1 + x2 = -0.1 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x2 = -0.1 + 1 Combine like terms: -1 + 1 = 0 0 + x2 = -0.1 + 1 x2 = -0.1 + 1 Combine like terms: -0.1 + 1 = 0.9 x2 = 0.9 Simplifying x2 = 0.9 Take the square root of each side: x = {-0.948683298, 0.948683298}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.048808848, 1.048808848, -0.948683298, 0.948683298}
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