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Simplifying 7x4 + 12x2 = 26 Reorder the terms: 12x2 + 7x4 = 26 Solving 12x2 + 7x4 = 26 Solving for variable 'x'. Reorder the terms: -26 + 12x2 + 7x4 = 26 + -26 Combine like terms: 26 + -26 = 0 -26 + 12x2 + 7x4 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -3.714285714 + 1.714285714x2 + x4 = 0 Move the constant term to the right: Add '3.714285714' to each side of the equation. -3.714285714 + 1.714285714x2 + 3.714285714 + x4 = 0 + 3.714285714 Reorder the terms: -3.714285714 + 3.714285714 + 1.714285714x2 + x4 = 0 + 3.714285714 Combine like terms: -3.714285714 + 3.714285714 = 0.000000000 0.000000000 + 1.714285714x2 + x4 = 0 + 3.714285714 1.714285714x2 + x4 = 0 + 3.714285714 Combine like terms: 0 + 3.714285714 = 3.714285714 1.714285714x2 + x4 = 3.714285714 The x term is 1.714285714x2. Take half its coefficient (0.857142857). Square it (0.7346938773) and add it to both sides. Add '0.7346938773' to each side of the equation. 1.714285714x2 + 0.7346938773 + x4 = 3.714285714 + 0.7346938773 Reorder the terms: 0.7346938773 + 1.714285714x2 + x4 = 3.714285714 + 0.7346938773 Combine like terms: 3.714285714 + 0.7346938773 = 4.4489795913 0.7346938773 + 1.714285714x2 + x4 = 4.4489795913 Factor a perfect square on the left side: (x2 + 0.857142857)(x2 + 0.857142857) = 4.4489795913 Calculate the square root of the right side: 2.109260437 Break this problem into two subproblems by setting (x2 + 0.857142857) equal to 2.109260437 and -2.109260437.Subproblem 1
x2 + 0.857142857 = 2.109260437 Simplifying x2 + 0.857142857 = 2.109260437 Reorder the terms: 0.857142857 + x2 = 2.109260437 Solving 0.857142857 + x2 = 2.109260437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.857142857' to each side of the equation. 0.857142857 + -0.857142857 + x2 = 2.109260437 + -0.857142857 Combine like terms: 0.857142857 + -0.857142857 = 0.000000000 0.000000000 + x2 = 2.109260437 + -0.857142857 x2 = 2.109260437 + -0.857142857 Combine like terms: 2.109260437 + -0.857142857 = 1.25211758 x2 = 1.25211758 Simplifying x2 = 1.25211758 Take the square root of each side: x = {-1.118980599, 1.118980599}Subproblem 2
x2 + 0.857142857 = -2.109260437 Simplifying x2 + 0.857142857 = -2.109260437 Reorder the terms: 0.857142857 + x2 = -2.109260437 Solving 0.857142857 + x2 = -2.109260437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.857142857' to each side of the equation. 0.857142857 + -0.857142857 + x2 = -2.109260437 + -0.857142857 Combine like terms: 0.857142857 + -0.857142857 = 0.000000000 0.000000000 + x2 = -2.109260437 + -0.857142857 x2 = -2.109260437 + -0.857142857 Combine like terms: -2.109260437 + -0.857142857 = -2.966403294 x2 = -2.966403294 Simplifying x2 = -2.966403294 Reorder the terms: 2.966403294 + x2 = -2.966403294 + 2.966403294 Combine like terms: -2.966403294 + 2.966403294 = 0.000000000 2.966403294 + 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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