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Simplifying 9x4 = 13x2 + 4 Reorder the terms: 9x4 = 4 + 13x2 Solving 9x4 = 4 + 13x2 Solving for variable 'x'. Reorder the terms: -4 + -13x2 + 9x4 = 4 + 13x2 + -4 + -13x2 Reorder the terms: -4 + -13x2 + 9x4 = 4 + -4 + 13x2 + -13x2 Combine like terms: 4 + -4 = 0 -4 + -13x2 + 9x4 = 0 + 13x2 + -13x2 -4 + -13x2 + 9x4 = 13x2 + -13x2 Combine like terms: 13x2 + -13x2 = 0 -4 + -13x2 + 9x4 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.4444444444 + -1.444444444x2 + x4 = 0 Move the constant term to the right: Add '0.4444444444' to each side of the equation. -0.4444444444 + -1.444444444x2 + 0.4444444444 + x4 = 0 + 0.4444444444 Reorder the terms: -0.4444444444 + 0.4444444444 + -1.444444444x2 + x4 = 0 + 0.4444444444 Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000 0.0000000000 + -1.444444444x2 + x4 = 0 + 0.4444444444 -1.444444444x2 + x4 = 0 + 0.4444444444 Combine like terms: 0 + 0.4444444444 = 0.4444444444 -1.444444444x2 + x4 = 0.4444444444 The x term is -1.444444444x2. Take half its coefficient (-0.722222222). Square it (0.5216049380) and add it to both sides. Add '0.5216049380' to each side of the equation. -1.444444444x2 + 0.5216049380 + x4 = 0.4444444444 + 0.5216049380 Reorder the terms: 0.5216049380 + -1.444444444x2 + x4 = 0.4444444444 + 0.5216049380 Combine like terms: 0.4444444444 + 0.5216049380 = 0.9660493824 0.5216049380 + -1.444444444x2 + x4 = 0.9660493824 Factor a perfect square on the left side: (x2 + -0.722222222)(x2 + -0.722222222) = 0.9660493824 Calculate the square root of the right side: 0.982878112 Break this problem into two subproblems by setting (x2 + -0.722222222) equal to 0.982878112 and -0.982878112.Subproblem 1
x2 + -0.722222222 = 0.982878112 Simplifying x2 + -0.722222222 = 0.982878112 Reorder the terms: -0.722222222 + x2 = 0.982878112 Solving -0.722222222 + x2 = 0.982878112 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.722222222' to each side of the equation. -0.722222222 + 0.722222222 + x2 = 0.982878112 + 0.722222222 Combine like terms: -0.722222222 + 0.722222222 = 0.000000000 0.000000000 + x2 = 0.982878112 + 0.722222222 x2 = 0.982878112 + 0.722222222 Combine like terms: 0.982878112 + 0.722222222 = 1.705100334 x2 = 1.705100334 Simplifying x2 = 1.705100334 Take the square root of each side: x = {-1.305794905, 1.305794905}Subproblem 2
x2 + -0.722222222 = -0.982878112 Simplifying x2 + -0.722222222 = -0.982878112 Reorder the terms: -0.722222222 + x2 = -0.982878112 Solving -0.722222222 + x2 = -0.982878112 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.722222222' to each side of the equation. -0.722222222 + 0.722222222 + x2 = -0.982878112 + 0.722222222 Combine like terms: -0.722222222 + 0.722222222 = 0.000000000 0.000000000 + x2 = -0.982878112 + 0.722222222 x2 = -0.982878112 + 0.722222222 Combine like terms: -0.982878112 + 0.722222222 = -0.26065589 x2 = -0.26065589 Simplifying x2 = -0.26065589 Reorder the terms: 0.26065589 + x2 = -0.26065589 + 0.26065589 Combine like terms: -0.26065589 + 0.26065589 = 0.00000000 0.26065589 + x2 = 0.00000000 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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