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Simplifying 2.51x4 + 1.8x2 + -6 = 0 Reorder the terms: -6 + 1.8x2 + 2.51x4 = 0 Solving -6 + 1.8x2 + 2.51x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2.51 the coefficient of the squared term: Divide each side by '2.51'. -2.390438247 + 0.7171314741x2 + x4 = 0 Move the constant term to the right: Add '2.390438247' to each side of the equation. -2.390438247 + 0.7171314741x2 + 2.390438247 + x4 = 0 + 2.390438247 Reorder the terms: -2.390438247 + 2.390438247 + 0.7171314741x2 + x4 = 0 + 2.390438247 Combine like terms: -2.390438247 + 2.390438247 = 0.000000000 0.000000000 + 0.7171314741x2 + x4 = 0 + 2.390438247 0.7171314741x2 + x4 = 0 + 2.390438247 Combine like terms: 0 + 2.390438247 = 2.390438247 0.7171314741x2 + x4 = 2.390438247 The x term is 0.7171314741x2. Take half its coefficient (0.3585657371). Square it (0.1285693878) and add it to both sides. Add '0.1285693878' to each side of the equation. 0.7171314741x2 + 0.1285693878 + x4 = 2.390438247 + 0.1285693878 Reorder the terms: 0.1285693878 + 0.7171314741x2 + x4 = 2.390438247 + 0.1285693878 Combine like terms: 2.390438247 + 0.1285693878 = 2.5190076348 0.1285693878 + 0.7171314741x2 + x4 = 2.5190076348 Factor a perfect square on the left side: (x2 + 0.3585657371)(x2 + 0.3585657371) = 2.5190076348 Calculate the square root of the right side: 1.58713819 Break this problem into two subproblems by setting (x2 + 0.3585657371) equal to 1.58713819 and -1.58713819.Subproblem 1
x2 + 0.3585657371 = 1.58713819 Simplifying x2 + 0.3585657371 = 1.58713819 Reorder the terms: 0.3585657371 + x2 = 1.58713819 Solving 0.3585657371 + x2 = 1.58713819 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3585657371' to each side of the equation. 0.3585657371 + -0.3585657371 + x2 = 1.58713819 + -0.3585657371 Combine like terms: 0.3585657371 + -0.3585657371 = 0.0000000000 0.0000000000 + x2 = 1.58713819 + -0.3585657371 x2 = 1.58713819 + -0.3585657371 Combine like terms: 1.58713819 + -0.3585657371 = 1.2285724529 x2 = 1.2285724529 Simplifying x2 = 1.2285724529 Take the square root of each side: x = {-1.108409876, 1.108409876}Subproblem 2
x2 + 0.3585657371 = -1.58713819 Simplifying x2 + 0.3585657371 = -1.58713819 Reorder the terms: 0.3585657371 + x2 = -1.58713819 Solving 0.3585657371 + x2 = -1.58713819 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3585657371' to each side of the equation. 0.3585657371 + -0.3585657371 + x2 = -1.58713819 + -0.3585657371 Combine like terms: 0.3585657371 + -0.3585657371 = 0.0000000000 0.0000000000 + x2 = -1.58713819 + -0.3585657371 x2 = -1.58713819 + -0.3585657371 Combine like terms: -1.58713819 + -0.3585657371 = -1.9457039271 x2 = -1.9457039271 Simplifying x2 = -1.9457039271 Reorder the terms: 1.9457039271 + x2 = -1.9457039271 + 1.9457039271 Combine like terms: -1.9457039271 + 1.9457039271 = 0.0000000000 1.9457039271 + 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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