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Simplifying 2x3 + 49x = 14x2 Reorder the terms: 49x + 2x3 = 14x2 Solving 49x + 2x3 = 14x2 Solving for variable 'x'. Reorder the terms: 49x + -14x2 + 2x3 = 14x2 + -14x2 Combine like terms: 14x2 + -14x2 = 0 49x + -14x2 + 2x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(49 + -14x + 2x2) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(49 + -14x + 2x2)' equal to zero and attempt to solve: Simplifying 49 + -14x + 2x2 = 0 Solving 49 + -14x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 24.5 + -7x + x2 = 0 Move the constant term to the right: Add '-24.5' to each side of the equation. 24.5 + -7x + -24.5 + x2 = 0 + -24.5 Reorder the terms: 24.5 + -24.5 + -7x + x2 = 0 + -24.5 Combine like terms: 24.5 + -24.5 = 0.0 0.0 + -7x + x2 = 0 + -24.5 -7x + x2 = 0 + -24.5 Combine like terms: 0 + -24.5 = -24.5 -7x + x2 = -24.5 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = -24.5 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -24.5 + 12.25 Combine like terms: -24.5 + 12.25 = -12.25 12.25 + -7x + x2 = -12.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = -12.25 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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