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Simplifying -40x4 + -21x2 + 3 = 0 Reorder the terms: 3 + -21x2 + -40x4 = 0 Solving 3 + -21x2 + -40x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -40 the coefficient of the squared term: Divide each side by '-40'. -0.075 + 0.525x2 + x4 = 0 Move the constant term to the right: Add '0.075' to each side of the equation. -0.075 + 0.525x2 + 0.075 + x4 = 0 + 0.075 Reorder the terms: -0.075 + 0.075 + 0.525x2 + x4 = 0 + 0.075 Combine like terms: -0.075 + 0.075 = 0.000 0.000 + 0.525x2 + x4 = 0 + 0.075 0.525x2 + x4 = 0 + 0.075 Combine like terms: 0 + 0.075 = 0.075 0.525x2 + x4 = 0.075 The x term is 0.525x2. Take half its coefficient (0.2625). Square it (0.06890625) and add it to both sides. Add '0.06890625' to each side of the equation. 0.525x2 + 0.06890625 + x4 = 0.075 + 0.06890625 Reorder the terms: 0.06890625 + 0.525x2 + x4 = 0.075 + 0.06890625 Combine like terms: 0.075 + 0.06890625 = 0.14390625 0.06890625 + 0.525x2 + x4 = 0.14390625 Factor a perfect square on the left side: (x2 + 0.2625)(x2 + 0.2625) = 0.14390625 Calculate the square root of the right side: 0.379349773 Break this problem into two subproblems by setting (x2 + 0.2625) equal to 0.379349773 and -0.379349773.Subproblem 1
x2 + 0.2625 = 0.379349773 Simplifying x2 + 0.2625 = 0.379349773 Reorder the terms: 0.2625 + x2 = 0.379349773 Solving 0.2625 + x2 = 0.379349773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2625' to each side of the equation. 0.2625 + -0.2625 + x2 = 0.379349773 + -0.2625 Combine like terms: 0.2625 + -0.2625 = 0.0000 0.0000 + x2 = 0.379349773 + -0.2625 x2 = 0.379349773 + -0.2625 Combine like terms: 0.379349773 + -0.2625 = 0.116849773 x2 = 0.116849773 Simplifying x2 = 0.116849773 Take the square root of each side: x = {-0.341832961, 0.341832961}Subproblem 2
x2 + 0.2625 = -0.379349773 Simplifying x2 + 0.2625 = -0.379349773 Reorder the terms: 0.2625 + x2 = -0.379349773 Solving 0.2625 + x2 = -0.379349773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2625' to each side of the equation. 0.2625 + -0.2625 + x2 = -0.379349773 + -0.2625 Combine like terms: 0.2625 + -0.2625 = 0.0000 0.0000 + x2 = -0.379349773 + -0.2625 x2 = -0.379349773 + -0.2625 Combine like terms: -0.379349773 + -0.2625 = -0.641849773 x2 = -0.641849773 Simplifying x2 = -0.641849773 Reorder the terms: 0.641849773 + x2 = -0.641849773 + 0.641849773 Combine like terms: -0.641849773 + 0.641849773 = 0.000000000 0.641849773 + x2 = 0.000000000 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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