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Simplifying 16x4 + -9x2 = 6 Reorder the terms: -9x2 + 16x4 = 6 Solving -9x2 + 16x4 = 6 Solving for variable 'x'. Reorder the terms: -6 + -9x2 + 16x4 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + -9x2 + 16x4 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.375 + -0.5625x2 + x4 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -0.5625x2 + 0.375 + x4 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -0.5625x2 + x4 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -0.5625x2 + x4 = 0 + 0.375 -0.5625x2 + x4 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -0.5625x2 + x4 = 0.375 The x term is -0.5625x2. Take half its coefficient (-0.28125). Square it (0.0791015625) and add it to both sides. Add '0.0791015625' to each side of the equation. -0.5625x2 + 0.0791015625 + x4 = 0.375 + 0.0791015625 Reorder the terms: 0.0791015625 + -0.5625x2 + x4 = 0.375 + 0.0791015625 Combine like terms: 0.375 + 0.0791015625 = 0.4541015625 0.0791015625 + -0.5625x2 + x4 = 0.4541015625 Factor a perfect square on the left side: (x2 + -0.28125)(x2 + -0.28125) = 0.4541015625 Calculate the square root of the right side: 0.673870583 Break this problem into two subproblems by setting (x2 + -0.28125) equal to 0.673870583 and -0.673870583.Subproblem 1
x2 + -0.28125 = 0.673870583 Simplifying x2 + -0.28125 = 0.673870583 Reorder the terms: -0.28125 + x2 = 0.673870583 Solving -0.28125 + x2 = 0.673870583 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.28125' to each side of the equation. -0.28125 + 0.28125 + x2 = 0.673870583 + 0.28125 Combine like terms: -0.28125 + 0.28125 = 0.00000 0.00000 + x2 = 0.673870583 + 0.28125 x2 = 0.673870583 + 0.28125 Combine like terms: 0.673870583 + 0.28125 = 0.955120583 x2 = 0.955120583 Simplifying x2 = 0.955120583 Take the square root of each side: x = {-0.977302708, 0.977302708}Subproblem 2
x2 + -0.28125 = -0.673870583 Simplifying x2 + -0.28125 = -0.673870583 Reorder the terms: -0.28125 + x2 = -0.673870583 Solving -0.28125 + x2 = -0.673870583 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.28125' to each side of the equation. -0.28125 + 0.28125 + x2 = -0.673870583 + 0.28125 Combine like terms: -0.28125 + 0.28125 = 0.00000 0.00000 + x2 = -0.673870583 + 0.28125 x2 = -0.673870583 + 0.28125 Combine like terms: -0.673870583 + 0.28125 = -0.392620583 x2 = -0.392620583 Simplifying x2 = -0.392620583 Reorder the terms: 0.392620583 + x2 = -0.392620583 + 0.392620583 Combine like terms: -0.392620583 + 0.392620583 = 0.000000000 0.392620583 + 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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