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Simplifying 2x4 + -10x2 + 3 = 0 Reorder the terms: 3 + -10x2 + 2x4 = 0 Solving 3 + -10x2 + 2x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1.5 + -5x2 + x4 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -5x2 + -1.5 + x4 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -5x2 + x4 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -5x2 + x4 = 0 + -1.5 -5x2 + x4 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -5x2 + x4 = -1.5 The x term is -5x2. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x2 + 6.25 + x4 = -1.5 + 6.25 Reorder the terms: 6.25 + -5x2 + x4 = -1.5 + 6.25 Combine like terms: -1.5 + 6.25 = 4.75 6.25 + -5x2 + x4 = 4.75 Factor a perfect square on the left side: (x2 + -2.5)(x2 + -2.5) = 4.75 Calculate the square root of the right side: 2.179449472 Break this problem into two subproblems by setting (x2 + -2.5) equal to 2.179449472 and -2.179449472.Subproblem 1
x2 + -2.5 = 2.179449472 Simplifying x2 + -2.5 = 2.179449472 Reorder the terms: -2.5 + x2 = 2.179449472 Solving -2.5 + x2 = 2.179449472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x2 = 2.179449472 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x2 = 2.179449472 + 2.5 x2 = 2.179449472 + 2.5 Combine like terms: 2.179449472 + 2.5 = 4.679449472 x2 = 4.679449472 Simplifying x2 = 4.679449472 Take the square root of each side: x = {-2.163203521, 2.163203521}Subproblem 2
x2 + -2.5 = -2.179449472 Simplifying x2 + -2.5 = -2.179449472 Reorder the terms: -2.5 + x2 = -2.179449472 Solving -2.5 + x2 = -2.179449472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x2 = -2.179449472 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x2 = -2.179449472 + 2.5 x2 = -2.179449472 + 2.5 Combine like terms: -2.179449472 + 2.5 = 0.320550528 x2 = 0.320550528 Simplifying x2 = 0.320550528 Take the square root of each side: x = {-0.566171818, 0.566171818}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.163203521, 2.163203521, -0.566171818, 0.566171818}
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