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Simplifying 4x4 + 15x2 + -72 = 0 Reorder the terms: -72 + 15x2 + 4x4 = 0 Solving -72 + 15x2 + 4x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -18 + 3.75x2 + x4 = 0 Move the constant term to the right: Add '18' to each side of the equation. -18 + 3.75x2 + 18 + x4 = 0 + 18 Reorder the terms: -18 + 18 + 3.75x2 + x4 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 3.75x2 + x4 = 0 + 18 3.75x2 + x4 = 0 + 18 Combine like terms: 0 + 18 = 18 3.75x2 + x4 = 18 The x term is 3.75x2. Take half its coefficient (1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. 3.75x2 + 3.515625 + x4 = 18 + 3.515625 Reorder the terms: 3.515625 + 3.75x2 + x4 = 18 + 3.515625 Combine like terms: 18 + 3.515625 = 21.515625 3.515625 + 3.75x2 + x4 = 21.515625 Factor a perfect square on the left side: (x2 + 1.875)(x2 + 1.875) = 21.515625 Calculate the square root of the right side: 4.638493829 Break this problem into two subproblems by setting (x2 + 1.875) equal to 4.638493829 and -4.638493829.Subproblem 1
x2 + 1.875 = 4.638493829 Simplifying x2 + 1.875 = 4.638493829 Reorder the terms: 1.875 + x2 = 4.638493829 Solving 1.875 + x2 = 4.638493829 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + x2 = 4.638493829 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x2 = 4.638493829 + -1.875 x2 = 4.638493829 + -1.875 Combine like terms: 4.638493829 + -1.875 = 2.763493829 x2 = 2.763493829 Simplifying x2 = 2.763493829 Take the square root of each side: x = {-1.662375959, 1.662375959}Subproblem 2
x2 + 1.875 = -4.638493829 Simplifying x2 + 1.875 = -4.638493829 Reorder the terms: 1.875 + x2 = -4.638493829 Solving 1.875 + x2 = -4.638493829 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + x2 = -4.638493829 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x2 = -4.638493829 + -1.875 x2 = -4.638493829 + -1.875 Combine like terms: -4.638493829 + -1.875 = -6.513493829 x2 = -6.513493829 Simplifying x2 = -6.513493829 Reorder the terms: 6.513493829 + x2 = -6.513493829 + 6.513493829 Combine like terms: -6.513493829 + 6.513493829 = 0.000000000 6.513493829 + 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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