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Simplifying 13x4 + -5x2 + -17 = 0 Reorder the terms: -17 + -5x2 + 13x4 = 0 Solving -17 + -5x2 + 13x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -1.307692308 + -0.3846153846x2 + x4 = 0 Move the constant term to the right: Add '1.307692308' to each side of the equation. -1.307692308 + -0.3846153846x2 + 1.307692308 + x4 = 0 + 1.307692308 Reorder the terms: -1.307692308 + 1.307692308 + -0.3846153846x2 + x4 = 0 + 1.307692308 Combine like terms: -1.307692308 + 1.307692308 = 0.000000000 0.000000000 + -0.3846153846x2 + x4 = 0 + 1.307692308 -0.3846153846x2 + x4 = 0 + 1.307692308 Combine like terms: 0 + 1.307692308 = 1.307692308 -0.3846153846x2 + x4 = 1.307692308 The x term is -0.3846153846x2. Take half its coefficient (-0.1923076923). Square it (0.03698224852) and add it to both sides. Add '0.03698224852' to each side of the equation. -0.3846153846x2 + 0.03698224852 + x4 = 1.307692308 + 0.03698224852 Reorder the terms: 0.03698224852 + -0.3846153846x2 + x4 = 1.307692308 + 0.03698224852 Combine like terms: 1.307692308 + 0.03698224852 = 1.34467455652 0.03698224852 + -0.3846153846x2 + x4 = 1.34467455652 Factor a perfect square on the left side: (x2 + -0.1923076923)(x2 + -0.1923076923) = 1.34467455652 Calculate the square root of the right side: 1.159601033 Break this problem into two subproblems by setting (x2 + -0.1923076923) equal to 1.159601033 and -1.159601033.Subproblem 1
x2 + -0.1923076923 = 1.159601033 Simplifying x2 + -0.1923076923 = 1.159601033 Reorder the terms: -0.1923076923 + x2 = 1.159601033 Solving -0.1923076923 + x2 = 1.159601033 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1923076923' to each side of the equation. -0.1923076923 + 0.1923076923 + x2 = 1.159601033 + 0.1923076923 Combine like terms: -0.1923076923 + 0.1923076923 = 0.0000000000 0.0000000000 + x2 = 1.159601033 + 0.1923076923 x2 = 1.159601033 + 0.1923076923 Combine like terms: 1.159601033 + 0.1923076923 = 1.3519087253 x2 = 1.3519087253 Simplifying x2 = 1.3519087253 Take the square root of each side: x = {-1.162716098, 1.162716098}Subproblem 2
x2 + -0.1923076923 = -1.159601033 Simplifying x2 + -0.1923076923 = -1.159601033 Reorder the terms: -0.1923076923 + x2 = -1.159601033 Solving -0.1923076923 + x2 = -1.159601033 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1923076923' to each side of the equation. -0.1923076923 + 0.1923076923 + x2 = -1.159601033 + 0.1923076923 Combine like terms: -0.1923076923 + 0.1923076923 = 0.0000000000 0.0000000000 + x2 = -1.159601033 + 0.1923076923 x2 = -1.159601033 + 0.1923076923 Combine like terms: -1.159601033 + 0.1923076923 = -0.9672933407 x2 = -0.9672933407 Simplifying x2 = -0.9672933407 Reorder the terms: 0.9672933407 + x2 = -0.9672933407 + 0.9672933407 Combine like terms: -0.9672933407 + 0.9672933407 = 0.0000000000 0.9672933407 + 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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