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Simplifying 4 * 625x4 + -100x2 + 4 + 275x2 + -22 + -3 = 0 Multiply 4 * 625 2500x4 + -100x2 + 4 + 275x2 + -22 + -3 = 0 Reorder the terms: 4 + -22 + -3 + -100x2 + 275x2 + 2500x4 = 0 Combine like terms: 4 + -22 = -18 -18 + -3 + -100x2 + 275x2 + 2500x4 = 0 Combine like terms: -18 + -3 = -21 -21 + -100x2 + 275x2 + 2500x4 = 0 Combine like terms: -100x2 + 275x2 = 175x2 -21 + 175x2 + 2500x4 = 0 Solving -21 + 175x2 + 2500x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2500 the coefficient of the squared term: Divide each side by '2500'. -0.0084 + 0.07x2 + x4 = 0.00 Move the constant term to the right: Add '0.0084' to each side of the equation. -0.0084 + 0.07x2 + 0.0084 + x4 = 0.00 + 0.0084 Reorder the terms: -0.0084 + 0.0084 + 0.07x2 + x4 = 0.00 + 0.0084 Combine like terms: -0.0084 + 0.0084 = 0.0000 0.0000 + 0.07x2 + x4 = 0.00 + 0.0084 0.07x2 + x4 = 0.00 + 0.0084 Combine like terms: 0.00 + 0.0084 = 0.0084 0.07x2 + x4 = 0.0084 The x term is 0.07x2. Take half its coefficient (0.035). Square it (0.001225) and add it to both sides. Add '0.001225' to each side of the equation. 0.07x2 + 0.001225 + x4 = 0.0084 + 0.001225 Reorder the terms: 0.001225 + 0.07x2 + x4 = 0.0084 + 0.001225 Combine like terms: 0.0084 + 0.001225 = 0.009625 0.001225 + 0.07x2 + x4 = 0.009625 Factor a perfect square on the left side: (x2 + 0.035)(x2 + 0.035) = 0.009625 Calculate the square root of the right side: 0.098107084 Break this problem into two subproblems by setting (x2 + 0.035) equal to 0.098107084 and -0.098107084.Subproblem 1
x2 + 0.035 = 0.098107084 Simplifying x2 + 0.035 = 0.098107084 Reorder the terms: 0.035 + x2 = 0.098107084 Solving 0.035 + x2 = 0.098107084 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.035' to each side of the equation. 0.035 + -0.035 + x2 = 0.098107084 + -0.035 Combine like terms: 0.035 + -0.035 = 0.000 0.000 + x2 = 0.098107084 + -0.035 x2 = 0.098107084 + -0.035 Combine like terms: 0.098107084 + -0.035 = 0.063107084 x2 = 0.063107084 Simplifying x2 = 0.063107084 Take the square root of each side: x = {-0.251211234, 0.251211234}Subproblem 2
x2 + 0.035 = -0.098107084 Simplifying x2 + 0.035 = -0.098107084 Reorder the terms: 0.035 + x2 = -0.098107084 Solving 0.035 + x2 = -0.098107084 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.035' to each side of the equation. 0.035 + -0.035 + x2 = -0.098107084 + -0.035 Combine like terms: 0.035 + -0.035 = 0.000 0.000 + x2 = -0.098107084 + -0.035 x2 = -0.098107084 + -0.035 Combine like terms: -0.098107084 + -0.035 = -0.133107084 x2 = -0.133107084 Simplifying x2 = -0.133107084 Reorder the terms: 0.133107084 + x2 = -0.133107084 + 0.133107084 Combine like terms: -0.133107084 + 0.133107084 = 0.000000000 0.133107084 + 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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