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Simplifying -15x4 + -18x2 + -4 = 0 Reorder the terms: -4 + -18x2 + -15x4 = 0 Solving -4 + -18x2 + -15x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(4 + 18x2 + 15x4) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(4 + 18x2 + 15x4)' equal to zero and attempt to solve: Simplifying 4 + 18x2 + 15x4 = 0 Solving 4 + 18x2 + 15x4 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. 0.2666666667 + 1.2x2 + x4 = 0 Move the constant term to the right: Add '-0.2666666667' to each side of the equation. 0.2666666667 + 1.2x2 + -0.2666666667 + x4 = 0 + -0.2666666667 Reorder the terms: 0.2666666667 + -0.2666666667 + 1.2x2 + x4 = 0 + -0.2666666667 Combine like terms: 0.2666666667 + -0.2666666667 = 0.0000000000 0.0000000000 + 1.2x2 + x4 = 0 + -0.2666666667 1.2x2 + x4 = 0 + -0.2666666667 Combine like terms: 0 + -0.2666666667 = -0.2666666667 1.2x2 + x4 = -0.2666666667 The x term is 1.2x2. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2x2 + 0.36 + x4 = -0.2666666667 + 0.36 Reorder the terms: 0.36 + 1.2x2 + x4 = -0.2666666667 + 0.36 Combine like terms: -0.2666666667 + 0.36 = 0.0933333333 0.36 + 1.2x2 + x4 = 0.0933333333 Factor a perfect square on the left side: (x2 + 0.6)(x2 + 0.6) = 0.0933333333 Calculate the square root of the right side: 0.305505046 Break this problem into two subproblems by setting (x2 + 0.6) equal to 0.305505046 and -0.305505046.Subproblem 1
x2 + 0.6 = 0.305505046 Simplifying x2 + 0.6 = 0.305505046 Reorder the terms: 0.6 + x2 = 0.305505046 Solving 0.6 + x2 = 0.305505046 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x2 = 0.305505046 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x2 = 0.305505046 + -0.6 x2 = 0.305505046 + -0.6 Combine like terms: 0.305505046 + -0.6 = -0.294494954 x2 = -0.294494954 Simplifying x2 = -0.294494954 Reorder the terms: 0.294494954 + x2 = -0.294494954 + 0.294494954 Combine like terms: -0.294494954 + 0.294494954 = 0.000000000 0.294494954 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x2 + 0.6 = -0.305505046 Simplifying x2 + 0.6 = -0.305505046 Reorder the terms: 0.6 + x2 = -0.305505046 Solving 0.6 + x2 = -0.305505046 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x2 = -0.305505046 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x2 = -0.305505046 + -0.6 x2 = -0.305505046 + -0.6 Combine like terms: -0.305505046 + -0.6 = -0.905505046 x2 = -0.905505046 Simplifying x2 = -0.905505046 Reorder the terms: 0.905505046 + x2 = -0.905505046 + 0.905505046 Combine like terms: -0.905505046 + 0.905505046 = 0.000000000 0.905505046 + 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. 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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