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Simplifying 36x4 + -25x2 = 4 Reorder the terms: -25x2 + 36x4 = 4 Solving -25x2 + 36x4 = 4 Solving for variable 'x'. Reorder the terms: -4 + -25x2 + 36x4 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + -25x2 + 36x4 = 0 Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -0.1111111111 + -0.6944444444x2 + x4 = 0 Move the constant term to the right: Add '0.1111111111' to each side of the equation. -0.1111111111 + -0.6944444444x2 + 0.1111111111 + x4 = 0 + 0.1111111111 Reorder the terms: -0.1111111111 + 0.1111111111 + -0.6944444444x2 + x4 = 0 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + -0.6944444444x2 + x4 = 0 + 0.1111111111 -0.6944444444x2 + x4 = 0 + 0.1111111111 Combine like terms: 0 + 0.1111111111 = 0.1111111111 -0.6944444444x2 + x4 = 0.1111111111 The x term is -0.6944444444x2. Take half its coefficient (-0.3472222222). Square it (0.1205632716) and add it to both sides. Add '0.1205632716' to each side of the equation. -0.6944444444x2 + 0.1205632716 + x4 = 0.1111111111 + 0.1205632716 Reorder the terms: 0.1205632716 + -0.6944444444x2 + x4 = 0.1111111111 + 0.1205632716 Combine like terms: 0.1111111111 + 0.1205632716 = 0.2316743827 0.1205632716 + -0.6944444444x2 + x4 = 0.2316743827 Factor a perfect square on the left side: (x2 + -0.3472222222)(x2 + -0.3472222222) = 0.2316743827 Calculate the square root of the right side: 0.481325651 Break this problem into two subproblems by setting (x2 + -0.3472222222) equal to 0.481325651 and -0.481325651.Subproblem 1
x2 + -0.3472222222 = 0.481325651 Simplifying x2 + -0.3472222222 = 0.481325651 Reorder the terms: -0.3472222222 + x2 = 0.481325651 Solving -0.3472222222 + x2 = 0.481325651 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3472222222' to each side of the equation. -0.3472222222 + 0.3472222222 + x2 = 0.481325651 + 0.3472222222 Combine like terms: -0.3472222222 + 0.3472222222 = 0.0000000000 0.0000000000 + x2 = 0.481325651 + 0.3472222222 x2 = 0.481325651 + 0.3472222222 Combine like terms: 0.481325651 + 0.3472222222 = 0.8285478732 x2 = 0.8285478732 Simplifying x2 = 0.8285478732 Take the square root of each side: x = {-0.910246051, 0.910246051}Subproblem 2
x2 + -0.3472222222 = -0.481325651 Simplifying x2 + -0.3472222222 = -0.481325651 Reorder the terms: -0.3472222222 + x2 = -0.481325651 Solving -0.3472222222 + x2 = -0.481325651 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3472222222' to each side of the equation. -0.3472222222 + 0.3472222222 + x2 = -0.481325651 + 0.3472222222 Combine like terms: -0.3472222222 + 0.3472222222 = 0.0000000000 0.0000000000 + x2 = -0.481325651 + 0.3472222222 x2 = -0.481325651 + 0.3472222222 Combine like terms: -0.481325651 + 0.3472222222 = -0.1341034288 x2 = -0.1341034288 Simplifying x2 = -0.1341034288 Reorder the terms: 0.1341034288 + x2 = -0.1341034288 + 0.1341034288 Combine like terms: -0.1341034288 + 0.1341034288 = 0.0000000000 0.1341034288 + x2 = 0.0000000000 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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