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Simplifying 3x4 + x2 = 0.5 Reorder the terms: x2 + 3x4 = 0.5 Solving x2 + 3x4 = 0.5 Solving for variable 'x'. Reorder the terms: -0.5 + x2 + 3x4 = 0.5 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 -0.5 + x2 + 3x4 = 0.0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -0.1666666667 + 0.3333333333x2 + x4 = 0.0 Move the constant term to the right: Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.3333333333x2 + 0.1666666667 + x4 = 0.0 + 0.1666666667 Reorder the terms: -0.1666666667 + 0.1666666667 + 0.3333333333x2 + x4 = 0.0 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + 0.3333333333x2 + x4 = 0.0 + 0.1666666667 0.3333333333x2 + x4 = 0.0 + 0.1666666667 Combine like terms: 0.0 + 0.1666666667 = 0.1666666667 0.3333333333x2 + x4 = 0.1666666667 The x term is x2. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.3333333333x2 + 0.25 + x4 = 0.1666666667 + 0.25 Reorder the terms: 0.25 + 0.3333333333x2 + x4 = 0.1666666667 + 0.25 Combine like terms: 0.1666666667 + 0.25 = 0.4166666667 0.25 + 0.3333333333x2 + x4 = 0.4166666667 Factor a perfect square on the left side: (x2 + 0.5)(x2 + 0.5) = 0.4166666667 Calculate the square root of the right side: 0.645497224 Break this problem into two subproblems by setting (x2 + 0.5) equal to 0.645497224 and -0.645497224.Subproblem 1
x2 + 0.5 = 0.645497224 Simplifying x2 + 0.5 = 0.645497224 Reorder the terms: 0.5 + x2 = 0.645497224 Solving 0.5 + x2 = 0.645497224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x2 = 0.645497224 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = 0.645497224 + -0.5 x2 = 0.645497224 + -0.5 Combine like terms: 0.645497224 + -0.5 = 0.145497224 x2 = 0.145497224 Simplifying x2 = 0.145497224 Take the square root of each side: x = {-0.381440984, 0.381440984}Subproblem 2
x2 + 0.5 = -0.645497224 Simplifying x2 + 0.5 = -0.645497224 Reorder the terms: 0.5 + x2 = -0.645497224 Solving 0.5 + x2 = -0.645497224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x2 = -0.645497224 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = -0.645497224 + -0.5 x2 = -0.645497224 + -0.5 Combine like terms: -0.645497224 + -0.5 = -1.145497224 x2 = -1.145497224 Simplifying x2 = -1.145497224 Reorder the terms: 1.145497224 + x2 = -1.145497224 + 1.145497224 Combine like terms: -1.145497224 + 1.145497224 = 0.000000000 1.145497224 + 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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