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Simplifying -17x4 + -4x2 + 18 = 0 Reorder the terms: 18 + -4x2 + -17x4 = 0 Solving 18 + -4x2 + -17x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -17 the coefficient of the squared term: Divide each side by '-17'. -1.058823529 + 0.2352941176x2 + x4 = 0 Move the constant term to the right: Add '1.058823529' to each side of the equation. -1.058823529 + 0.2352941176x2 + 1.058823529 + x4 = 0 + 1.058823529 Reorder the terms: -1.058823529 + 1.058823529 + 0.2352941176x2 + x4 = 0 + 1.058823529 Combine like terms: -1.058823529 + 1.058823529 = 0.000000000 0.000000000 + 0.2352941176x2 + x4 = 0 + 1.058823529 0.2352941176x2 + x4 = 0 + 1.058823529 Combine like terms: 0 + 1.058823529 = 1.058823529 0.2352941176x2 + x4 = 1.058823529 The x term is 0.2352941176x2. Take half its coefficient (0.1176470588). Square it (0.01384083044) and add it to both sides. Add '0.01384083044' to each side of the equation. 0.2352941176x2 + 0.01384083044 + x4 = 1.058823529 + 0.01384083044 Reorder the terms: 0.01384083044 + 0.2352941176x2 + x4 = 1.058823529 + 0.01384083044 Combine like terms: 1.058823529 + 0.01384083044 = 1.07266435944 0.01384083044 + 0.2352941176x2 + x4 = 1.07266435944 Factor a perfect square on the left side: (x2 + 0.1176470588)(x2 + 0.1176470588) = 1.07266435944 Calculate the square root of the right side: 1.035695109 Break this problem into two subproblems by setting (x2 + 0.1176470588) equal to 1.035695109 and -1.035695109.Subproblem 1
x2 + 0.1176470588 = 1.035695109 Simplifying x2 + 0.1176470588 = 1.035695109 Reorder the terms: 0.1176470588 + x2 = 1.035695109 Solving 0.1176470588 + x2 = 1.035695109 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1176470588' to each side of the equation. 0.1176470588 + -0.1176470588 + x2 = 1.035695109 + -0.1176470588 Combine like terms: 0.1176470588 + -0.1176470588 = 0.0000000000 0.0000000000 + x2 = 1.035695109 + -0.1176470588 x2 = 1.035695109 + -0.1176470588 Combine like terms: 1.035695109 + -0.1176470588 = 0.9180480502 x2 = 0.9180480502 Simplifying x2 = 0.9180480502 Take the square root of each side: x = {-0.95814824, 0.95814824}Subproblem 2
x2 + 0.1176470588 = -1.035695109 Simplifying x2 + 0.1176470588 = -1.035695109 Reorder the terms: 0.1176470588 + x2 = -1.035695109 Solving 0.1176470588 + x2 = -1.035695109 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1176470588' to each side of the equation. 0.1176470588 + -0.1176470588 + x2 = -1.035695109 + -0.1176470588 Combine like terms: 0.1176470588 + -0.1176470588 = 0.0000000000 0.0000000000 + x2 = -1.035695109 + -0.1176470588 x2 = -1.035695109 + -0.1176470588 Combine like terms: -1.035695109 + -0.1176470588 = -1.1533421678 x2 = -1.1533421678 Simplifying x2 = -1.1533421678 Reorder the terms: 1.1533421678 + x2 = -1.1533421678 + 1.1533421678 Combine like terms: -1.1533421678 + 1.1533421678 = 0.0000000000 1.1533421678 + 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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