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Simplifying 25x4z + 15x3z + 5x2z = 0 Reorder the terms: 5x2z + 15x3z + 25x4z = 0 Solving 5x2z + 15x3z + 25x4z = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5x2z'. 5x2z(1 + 3x + 5x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'x2z' equal to zero and attempt to solve: Simplifying x2z = 0 Solving x2z = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2z = 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 '(1 + 3x + 5x2)' equal to zero and attempt to solve: Simplifying 1 + 3x + 5x2 = 0 Solving 1 + 3x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.2 + 0.6x + x2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + 0.6x + -0.2 + x2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + 0.6x + x2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + 0.6x + x2 = 0 + -0.2 0.6x + x2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 0.6x + x2 = -0.2 The x term is 0.6x. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6x + 0.09 + x2 = -0.2 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = -0.2 + 0.09 Combine like terms: -0.2 + 0.09 = -0.11 0.09 + 0.6x + x2 = -0.11 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = -0.11 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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