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Simplifying 4x4 + 13x2 + -6 = 0 Reorder the terms: -6 + 13x2 + 4x4 = 0 Solving -6 + 13x2 + 4x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.5 + 3.25x2 + x4 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 3.25x2 + 1.5 + x4 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + 3.25x2 + x4 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 3.25x2 + x4 = 0 + 1.5 3.25x2 + x4 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 3.25x2 + x4 = 1.5 The x term is 3.25x2. Take half its coefficient (1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. 3.25x2 + 2.640625 + x4 = 1.5 + 2.640625 Reorder the terms: 2.640625 + 3.25x2 + x4 = 1.5 + 2.640625 Combine like terms: 1.5 + 2.640625 = 4.140625 2.640625 + 3.25x2 + x4 = 4.140625 Factor a perfect square on the left side: (x2 + 1.625)(x2 + 1.625) = 4.140625 Calculate the square root of the right side: 2.034852575 Break this problem into two subproblems by setting (x2 + 1.625) equal to 2.034852575 and -2.034852575.Subproblem 1
x2 + 1.625 = 2.034852575 Simplifying x2 + 1.625 = 2.034852575 Reorder the terms: 1.625 + x2 = 2.034852575 Solving 1.625 + x2 = 2.034852575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + x2 = 2.034852575 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x2 = 2.034852575 + -1.625 x2 = 2.034852575 + -1.625 Combine like terms: 2.034852575 + -1.625 = 0.409852575 x2 = 0.409852575 Simplifying x2 = 0.409852575 Take the square root of each side: x = {-0.640197294, 0.640197294}Subproblem 2
x2 + 1.625 = -2.034852575 Simplifying x2 + 1.625 = -2.034852575 Reorder the terms: 1.625 + x2 = -2.034852575 Solving 1.625 + x2 = -2.034852575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + x2 = -2.034852575 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x2 = -2.034852575 + -1.625 x2 = -2.034852575 + -1.625 Combine like terms: -2.034852575 + -1.625 = -3.659852575 x2 = -3.659852575 Simplifying x2 = -3.659852575 Reorder the terms: 3.659852575 + x2 = -3.659852575 + 3.659852575 Combine like terms: -3.659852575 + 3.659852575 = 0.000000000 3.659852575 + 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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