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Simplifying 56x5 + 46x4 + 30x3 = 0 Reorder the terms: 30x3 + 46x4 + 56x5 = 0 Solving 30x3 + 46x4 + 56x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x3'. 2x3(15 + 23x + 28x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x3' equal to zero and attempt to solve: Simplifying x3 = 0 Solving x3 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(15 + 23x + 28x2)' equal to zero and attempt to solve: Simplifying 15 + 23x + 28x2 = 0 Solving 15 + 23x + 28x2 = 0 Begin completing the square. Divide all terms by 28 the coefficient of the squared term: Divide each side by '28'. 0.5357142857 + 0.8214285714x + x2 = 0 Move the constant term to the right: Add '-0.5357142857' to each side of the equation. 0.5357142857 + 0.8214285714x + -0.5357142857 + x2 = 0 + -0.5357142857 Reorder the terms: 0.5357142857 + -0.5357142857 + 0.8214285714x + x2 = 0 + -0.5357142857 Combine like terms: 0.5357142857 + -0.5357142857 = 0.0000000000 0.0000000000 + 0.8214285714x + x2 = 0 + -0.5357142857 0.8214285714x + x2 = 0 + -0.5357142857 Combine like terms: 0 + -0.5357142857 = -0.5357142857 0.8214285714x + x2 = -0.5357142857 The x term is 0.8214285714x. Take half its coefficient (0.4107142857). Square it (0.1686862245) and add it to both sides. Add '0.1686862245' to each side of the equation. 0.8214285714x + 0.1686862245 + x2 = -0.5357142857 + 0.1686862245 Reorder the terms: 0.1686862245 + 0.8214285714x + x2 = -0.5357142857 + 0.1686862245 Combine like terms: -0.5357142857 + 0.1686862245 = -0.3670280612 0.1686862245 + 0.8214285714x + x2 = -0.3670280612 Factor a perfect square on the left side: (x + 0.4107142857)(x + 0.4107142857) = -0.3670280612 Can't calculate square root of the right side. 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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