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Simplifying 3x4 + -5 = 5x2 Reorder the terms: -5 + 3x4 = 5x2 Solving -5 + 3x4 = 5x2 Solving for variable 'x'. Reorder the terms: -5 + -5x2 + 3x4 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -5 + -5x2 + 3x4 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1.666666667 + -1.666666667x2 + x4 = 0 Move the constant term to the right: Add '1.666666667' to each side of the equation. -1.666666667 + -1.666666667x2 + 1.666666667 + x4 = 0 + 1.666666667 Reorder the terms: -1.666666667 + 1.666666667 + -1.666666667x2 + x4 = 0 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + -1.666666667x2 + x4 = 0 + 1.666666667 -1.666666667x2 + x4 = 0 + 1.666666667 Combine like terms: 0 + 1.666666667 = 1.666666667 -1.666666667x2 + x4 = 1.666666667 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 = 1.666666667 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x2 + x4 = 1.666666667 + 0.6944444447 Combine like terms: 1.666666667 + 0.6944444447 = 2.3611111117 0.6944444447 + -1.666666667x2 + x4 = 2.3611111117 Factor a perfect square on the left side: (x2 + -0.8333333335)(x2 + -0.8333333335) = 2.3611111117 Calculate the square root of the right side: 1.536590743 Break this problem into two subproblems by setting (x2 + -0.8333333335) equal to 1.536590743 and -1.536590743.Subproblem 1
x2 + -0.8333333335 = 1.536590743 Simplifying x2 + -0.8333333335 = 1.536590743 Reorder the terms: -0.8333333335 + x2 = 1.536590743 Solving -0.8333333335 + x2 = 1.536590743 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 = 1.536590743 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x2 = 1.536590743 + 0.8333333335 x2 = 1.536590743 + 0.8333333335 Combine like terms: 1.536590743 + 0.8333333335 = 2.3699240765 x2 = 2.3699240765 Simplifying x2 = 2.3699240765 Take the square root of each side: x = {-1.539455773, 1.539455773}Subproblem 2
x2 + -0.8333333335 = -1.536590743 Simplifying x2 + -0.8333333335 = -1.536590743 Reorder the terms: -0.8333333335 + x2 = -1.536590743 Solving -0.8333333335 + x2 = -1.536590743 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 = -1.536590743 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x2 = -1.536590743 + 0.8333333335 x2 = -1.536590743 + 0.8333333335 Combine like terms: -1.536590743 + 0.8333333335 = -0.7032574095 x2 = -0.7032574095 Simplifying x2 = -0.7032574095 Reorder the terms: 0.7032574095 + x2 = -0.7032574095 + 0.7032574095 Combine like terms: -0.7032574095 + 0.7032574095 = 0.0000000000 0.7032574095 + 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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