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Simplifying 5x4 + -51x2 + 16 = 0 Reorder the terms: 16 + -51x2 + 5x4 = 0 Solving 16 + -51x2 + 5x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 3.2 + -10.2x2 + x4 = 0 Move the constant term to the right: Add '-3.2' to each side of the equation. 3.2 + -10.2x2 + -3.2 + x4 = 0 + -3.2 Reorder the terms: 3.2 + -3.2 + -10.2x2 + x4 = 0 + -3.2 Combine like terms: 3.2 + -3.2 = 0.0 0.0 + -10.2x2 + x4 = 0 + -3.2 -10.2x2 + x4 = 0 + -3.2 Combine like terms: 0 + -3.2 = -3.2 -10.2x2 + x4 = -3.2 The x term is -10.2x2. Take half its coefficient (-5.1). Square it (26.01) and add it to both sides. Add '26.01' to each side of the equation. -10.2x2 + 26.01 + x4 = -3.2 + 26.01 Reorder the terms: 26.01 + -10.2x2 + x4 = -3.2 + 26.01 Combine like terms: -3.2 + 26.01 = 22.81 26.01 + -10.2x2 + x4 = 22.81 Factor a perfect square on the left side: (x2 + -5.1)(x2 + -5.1) = 22.81 Calculate the square root of the right side: 4.775981575 Break this problem into two subproblems by setting (x2 + -5.1) equal to 4.775981575 and -4.775981575.Subproblem 1
x2 + -5.1 = 4.775981575 Simplifying x2 + -5.1 = 4.775981575 Reorder the terms: -5.1 + x2 = 4.775981575 Solving -5.1 + x2 = 4.775981575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.1' to each side of the equation. -5.1 + 5.1 + x2 = 4.775981575 + 5.1 Combine like terms: -5.1 + 5.1 = 0.0 0.0 + x2 = 4.775981575 + 5.1 x2 = 4.775981575 + 5.1 Combine like terms: 4.775981575 + 5.1 = 9.875981575 x2 = 9.875981575 Simplifying x2 = 9.875981575 Take the square root of each side: x = {-3.142607448, 3.142607448}Subproblem 2
x2 + -5.1 = -4.775981575 Simplifying x2 + -5.1 = -4.775981575 Reorder the terms: -5.1 + x2 = -4.775981575 Solving -5.1 + x2 = -4.775981575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.1' to each side of the equation. -5.1 + 5.1 + x2 = -4.775981575 + 5.1 Combine like terms: -5.1 + 5.1 = 0.0 0.0 + x2 = -4.775981575 + 5.1 x2 = -4.775981575 + 5.1 Combine like terms: -4.775981575 + 5.1 = 0.324018425 x2 = 0.324018425 Simplifying x2 = 0.324018425 Take the square root of each side: x = {-0.569226163, 0.569226163}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.142607448, 3.142607448, -0.569226163, 0.569226163}
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