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Simplifying 35X4 + -42X3 + 63X2 = 0 Reorder the terms: 63X2 + -42X3 + 35X4 = 0 Solving 63X2 + -42X3 + 35X4 = 0 Solving for variable 'X'. Factor out the Greatest Common Factor (GCF), '7X2'. 7X2(9 + -6X + 5X2) = 0 Ignore the factor 7.Subproblem 1
Set the factor 'X2' equal to zero and attempt to solve: Simplifying X2 = 0 Solving X2 = 0 Move all terms containing X to the left, all other terms to the right. Simplifying X2 = 0 Take the square root of each side: X = {0}Subproblem 2
Set the factor '(9 + -6X + 5X2)' equal to zero and attempt to solve: Simplifying 9 + -6X + 5X2 = 0 Solving 9 + -6X + 5X2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.8 + -1.2X + X2 = 0 Move the constant term to the right: Add '-1.8' to each side of the equation. 1.8 + -1.2X + -1.8 + X2 = 0 + -1.8 Reorder the terms: 1.8 + -1.8 + -1.2X + X2 = 0 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + -1.2X + X2 = 0 + -1.8 -1.2X + X2 = 0 + -1.8 Combine like terms: 0 + -1.8 = -1.8 -1.2X + X2 = -1.8 The X term is -1.2X. 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. -1.2X + 0.36 + X2 = -1.8 + 0.36 Reorder the terms: 0.36 + -1.2X + X2 = -1.8 + 0.36 Combine like terms: -1.8 + 0.36 = -1.44 0.36 + -1.2X + X2 = -1.44 Factor a perfect square on the left side: (X + -0.6)(X + -0.6) = -1.44 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.Solution
X = {0}
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