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Simplifying 0 = 1.25x4 + -6x2 + 2 Reorder the terms: 0 = 2 + -6x2 + 1.25x4 Solving 0 = 2 + -6x2 + 1.25x4 Solving for variable 'x'. Combine like terms: 0 + -2 = -2 -2 + 6x2 + -1.25x4 = 2 + -6x2 + 1.25x4 + -2 + 6x2 + -1.25x4 Reorder the terms: -2 + 6x2 + -1.25x4 = 2 + -2 + -6x2 + 6x2 + 1.25x4 + -1.25x4 Combine like terms: 2 + -2 = 0 -2 + 6x2 + -1.25x4 = 0 + -6x2 + 6x2 + 1.25x4 + -1.25x4 -2 + 6x2 + -1.25x4 = -6x2 + 6x2 + 1.25x4 + -1.25x4 Combine like terms: -6x2 + 6x2 = 0 -2 + 6x2 + -1.25x4 = 0 + 1.25x4 + -1.25x4 -2 + 6x2 + -1.25x4 = 1.25x4 + -1.25x4 Combine like terms: 1.25x4 + -1.25x4 = 0.00 -2 + 6x2 + -1.25x4 = 0.00 Begin completing the square. Divide all terms by -1.25 the coefficient of the squared term: Divide each side by '-1.25'. 1.6 + -4.8x2 + x4 = 0 Move the constant term to the right: Add '-1.6' to each side of the equation. 1.6 + -4.8x2 + -1.6 + x4 = 0 + -1.6 Reorder the terms: 1.6 + -1.6 + -4.8x2 + x4 = 0 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + -4.8x2 + x4 = 0 + -1.6 -4.8x2 + x4 = 0 + -1.6 Combine like terms: 0 + -1.6 = -1.6 -4.8x2 + x4 = -1.6 The x term is -4.8x2. Take half its coefficient (-2.4). Square it (5.76) and add it to both sides. Add '5.76' to each side of the equation. -4.8x2 + 5.76 + x4 = -1.6 + 5.76 Reorder the terms: 5.76 + -4.8x2 + x4 = -1.6 + 5.76 Combine like terms: -1.6 + 5.76 = 4.16 5.76 + -4.8x2 + x4 = 4.16 Factor a perfect square on the left side: (x2 + -2.4)(x2 + -2.4) = 4.16 Calculate the square root of the right side: 2.039607805 Break this problem into two subproblems by setting (x2 + -2.4) equal to 2.039607805 and -2.039607805.Subproblem 1
x2 + -2.4 = 2.039607805 Simplifying x2 + -2.4 = 2.039607805 Reorder the terms: -2.4 + x2 = 2.039607805 Solving -2.4 + x2 = 2.039607805 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.4' to each side of the equation. -2.4 + 2.4 + x2 = 2.039607805 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + x2 = 2.039607805 + 2.4 x2 = 2.039607805 + 2.4 Combine like terms: 2.039607805 + 2.4 = 4.439607805 x2 = 4.439607805 Simplifying x2 = 4.439607805 Take the square root of each side: x = {-2.107037685, 2.107037685}Subproblem 2
x2 + -2.4 = -2.039607805 Simplifying x2 + -2.4 = -2.039607805 Reorder the terms: -2.4 + x2 = -2.039607805 Solving -2.4 + x2 = -2.039607805 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.4' to each side of the equation. -2.4 + 2.4 + x2 = -2.039607805 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + x2 = -2.039607805 + 2.4 x2 = -2.039607805 + 2.4 Combine like terms: -2.039607805 + 2.4 = 0.360392195 x2 = 0.360392195 Simplifying x2 = 0.360392195 Take the square root of each side: x = {-0.60032674, 0.60032674}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.107037685, 2.107037685, -0.60032674, 0.60032674}
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