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Simplifying 5x4 + -24x2 + 2 = 0 Reorder the terms: 2 + -24x2 + 5x4 = 0 Solving 2 + -24x2 + 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'. 0.4 + -4.8x2 + x4 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + -4.8x2 + -0.4 + x4 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + -4.8x2 + x4 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + -4.8x2 + x4 = 0 + -0.4 -4.8x2 + x4 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 -4.8x2 + x4 = -0.4 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 = -0.4 + 5.76 Reorder the terms: 5.76 + -4.8x2 + x4 = -0.4 + 5.76 Combine like terms: -0.4 + 5.76 = 5.36 5.76 + -4.8x2 + x4 = 5.36 Factor a perfect square on the left side: (x2 + -2.4)(x2 + -2.4) = 5.36 Calculate the square root of the right side: 2.315167381 Break this problem into two subproblems by setting (x2 + -2.4) equal to 2.315167381 and -2.315167381.Subproblem 1
x2 + -2.4 = 2.315167381 Simplifying x2 + -2.4 = 2.315167381 Reorder the terms: -2.4 + x2 = 2.315167381 Solving -2.4 + x2 = 2.315167381 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 = 2.315167381 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + x2 = 2.315167381 + 2.4 x2 = 2.315167381 + 2.4 Combine like terms: 2.315167381 + 2.4 = 4.715167381 x2 = 4.715167381 Simplifying x2 = 4.715167381 Take the square root of each side: x = {-2.171443617, 2.171443617}Subproblem 2
x2 + -2.4 = -2.315167381 Simplifying x2 + -2.4 = -2.315167381 Reorder the terms: -2.4 + x2 = -2.315167381 Solving -2.4 + x2 = -2.315167381 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 = -2.315167381 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + x2 = -2.315167381 + 2.4 x2 = -2.315167381 + 2.4 Combine like terms: -2.315167381 + 2.4 = 0.084832619 x2 = 0.084832619 Simplifying x2 = 0.084832619 Take the square root of each side: x = {-0.291260397, 0.291260397}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.171443617, 2.171443617, -0.291260397, 0.291260397}
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