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Simplifying 3x4 + 5x2 + -30 = 0 Reorder the terms: -30 + 5x2 + 3x4 = 0 Solving -30 + 5x2 + 3x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -10 + 1.666666667x2 + x4 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + 1.666666667x2 + 10 + x4 = 0 + 10 Reorder the terms: -10 + 10 + 1.666666667x2 + x4 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 1.666666667x2 + x4 = 0 + 10 1.666666667x2 + x4 = 0 + 10 Combine like terms: 0 + 10 = 10 1.666666667x2 + x4 = 10 The x term is 1.666666667x2. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667x2 + 0.6944444447 + x4 = 10 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x2 + x4 = 10 + 0.6944444447 Combine like terms: 10 + 0.6944444447 = 10.6944444447 0.6944444447 + 1.666666667x2 + x4 = 10.6944444447 Factor a perfect square on the left side: (x2 + 0.8333333335)(x2 + 0.8333333335) = 10.6944444447 Calculate the square root of the right side: 3.270236145 Break this problem into two subproblems by setting (x2 + 0.8333333335) equal to 3.270236145 and -3.270236145.Subproblem 1
x2 + 0.8333333335 = 3.270236145 Simplifying x2 + 0.8333333335 = 3.270236145 Reorder the terms: 0.8333333335 + x2 = 3.270236145 Solving 0.8333333335 + x2 = 3.270236145 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x2 = 3.270236145 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x2 = 3.270236145 + -0.8333333335 x2 = 3.270236145 + -0.8333333335 Combine like terms: 3.270236145 + -0.8333333335 = 2.4369028115 x2 = 2.4369028115 Simplifying x2 = 2.4369028115 Take the square root of each side: x = {-1.561058235, 1.561058235}Subproblem 2
x2 + 0.8333333335 = -3.270236145 Simplifying x2 + 0.8333333335 = -3.270236145 Reorder the terms: 0.8333333335 + x2 = -3.270236145 Solving 0.8333333335 + x2 = -3.270236145 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x2 = -3.270236145 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x2 = -3.270236145 + -0.8333333335 x2 = -3.270236145 + -0.8333333335 Combine like terms: -3.270236145 + -0.8333333335 = -4.1035694785 x2 = -4.1035694785 Simplifying x2 = -4.1035694785 Reorder the terms: 4.1035694785 + x2 = -4.1035694785 + 4.1035694785 Combine like terms: -4.1035694785 + 4.1035694785 = 0.0000000000 4.1035694785 + x2 = 0.0000000000 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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