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Simplifying 5x4 + -12x2 = 27 Reorder the terms: -12x2 + 5x4 = 27 Solving -12x2 + 5x4 = 27 Solving for variable 'x'. Reorder the terms: -27 + -12x2 + 5x4 = 27 + -27 Combine like terms: 27 + -27 = 0 -27 + -12x2 + 5x4 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -5.4 + -2.4x2 + x4 = 0 Move the constant term to the right: Add '5.4' to each side of the equation. -5.4 + -2.4x2 + 5.4 + x4 = 0 + 5.4 Reorder the terms: -5.4 + 5.4 + -2.4x2 + x4 = 0 + 5.4 Combine like terms: -5.4 + 5.4 = 0.0 0.0 + -2.4x2 + x4 = 0 + 5.4 -2.4x2 + x4 = 0 + 5.4 Combine like terms: 0 + 5.4 = 5.4 -2.4x2 + x4 = 5.4 The x term is -2.4x2. Take half its coefficient (-1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. -2.4x2 + 1.44 + x4 = 5.4 + 1.44 Reorder the terms: 1.44 + -2.4x2 + x4 = 5.4 + 1.44 Combine like terms: 5.4 + 1.44 = 6.84 1.44 + -2.4x2 + x4 = 6.84 Factor a perfect square on the left side: (x2 + -1.2)(x2 + -1.2) = 6.84 Calculate the square root of the right side: 2.615339366 Break this problem into two subproblems by setting (x2 + -1.2) equal to 2.615339366 and -2.615339366.Subproblem 1
x2 + -1.2 = 2.615339366 Simplifying x2 + -1.2 = 2.615339366 Reorder the terms: -1.2 + x2 = 2.615339366 Solving -1.2 + x2 = 2.615339366 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x2 = 2.615339366 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x2 = 2.615339366 + 1.2 x2 = 2.615339366 + 1.2 Combine like terms: 2.615339366 + 1.2 = 3.815339366 x2 = 3.815339366 Simplifying x2 = 3.815339366 Take the square root of each side: x = {-1.953289371, 1.953289371}Subproblem 2
x2 + -1.2 = -2.615339366 Simplifying x2 + -1.2 = -2.615339366 Reorder the terms: -1.2 + x2 = -2.615339366 Solving -1.2 + x2 = -2.615339366 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x2 = -2.615339366 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x2 = -2.615339366 + 1.2 x2 = -2.615339366 + 1.2 Combine like terms: -2.615339366 + 1.2 = -1.415339366 x2 = -1.415339366 Simplifying x2 = -1.415339366 Reorder the terms: 1.415339366 + x2 = -1.415339366 + 1.415339366 Combine like terms: -1.415339366 + 1.415339366 = 0.000000000 1.415339366 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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