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Simplifying 14x4 + -7x2 = 3 Reorder the terms: -7x2 + 14x4 = 3 Solving -7x2 + 14x4 = 3 Solving for variable 'x'. Reorder the terms: -3 + -7x2 + 14x4 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + -7x2 + 14x4 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -0.2142857143 + -0.5x2 + x4 = 0 Move the constant term to the right: Add '0.2142857143' to each side of the equation. -0.2142857143 + -0.5x2 + 0.2142857143 + x4 = 0 + 0.2142857143 Reorder the terms: -0.2142857143 + 0.2142857143 + -0.5x2 + x4 = 0 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + -0.5x2 + x4 = 0 + 0.2142857143 -0.5x2 + x4 = 0 + 0.2142857143 Combine like terms: 0 + 0.2142857143 = 0.2142857143 -0.5x2 + x4 = 0.2142857143 The x term is -0.5x2. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x2 + 0.0625 + x4 = 0.2142857143 + 0.0625 Reorder the terms: 0.0625 + -0.5x2 + x4 = 0.2142857143 + 0.0625 Combine like terms: 0.2142857143 + 0.0625 = 0.2767857143 0.0625 + -0.5x2 + x4 = 0.2767857143 Factor a perfect square on the left side: (x2 + -0.25)(x2 + -0.25) = 0.2767857143 Calculate the square root of the right side: 0.526104281 Break this problem into two subproblems by setting (x2 + -0.25) equal to 0.526104281 and -0.526104281.Subproblem 1
x2 + -0.25 = 0.526104281 Simplifying x2 + -0.25 = 0.526104281 Reorder the terms: -0.25 + x2 = 0.526104281 Solving -0.25 + x2 = 0.526104281 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x2 = 0.526104281 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x2 = 0.526104281 + 0.25 x2 = 0.526104281 + 0.25 Combine like terms: 0.526104281 + 0.25 = 0.776104281 x2 = 0.776104281 Simplifying x2 = 0.776104281 Take the square root of each side: x = {-0.880967809, 0.880967809}Subproblem 2
x2 + -0.25 = -0.526104281 Simplifying x2 + -0.25 = -0.526104281 Reorder the terms: -0.25 + x2 = -0.526104281 Solving -0.25 + x2 = -0.526104281 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x2 = -0.526104281 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x2 = -0.526104281 + 0.25 x2 = -0.526104281 + 0.25 Combine like terms: -0.526104281 + 0.25 = -0.276104281 x2 = -0.276104281 Simplifying x2 = -0.276104281 Reorder the terms: 0.276104281 + x2 = -0.276104281 + 0.276104281 Combine like terms: -0.276104281 + 0.276104281 = 0.000000000 0.276104281 + 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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