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Simplifying 13x4 + -2x3 + 19x2 = 0 Reorder the terms: 19x2 + -2x3 + 13x4 = 0 Solving 19x2 + -2x3 + 13x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(19 + -2x + 13x2) = 0Subproblem 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 '(19 + -2x + 13x2)' equal to zero and attempt to solve: Simplifying 19 + -2x + 13x2 = 0 Solving 19 + -2x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. 1.461538462 + -0.1538461538x + x2 = 0 Move the constant term to the right: Add '-1.461538462' to each side of the equation. 1.461538462 + -0.1538461538x + -1.461538462 + x2 = 0 + -1.461538462 Reorder the terms: 1.461538462 + -1.461538462 + -0.1538461538x + x2 = 0 + -1.461538462 Combine like terms: 1.461538462 + -1.461538462 = 0.000000000 0.000000000 + -0.1538461538x + x2 = 0 + -1.461538462 -0.1538461538x + x2 = 0 + -1.461538462 Combine like terms: 0 + -1.461538462 = -1.461538462 -0.1538461538x + x2 = -1.461538462 The x term is -0.1538461538x. Take half its coefficient (-0.0769230769). Square it (0.005917159760) and add it to both sides. Add '0.005917159760' to each side of the equation. -0.1538461538x + 0.005917159760 + x2 = -1.461538462 + 0.005917159760 Reorder the terms: 0.005917159760 + -0.1538461538x + x2 = -1.461538462 + 0.005917159760 Combine like terms: -1.461538462 + 0.005917159760 = -1.45562130224 0.005917159760 + -0.1538461538x + x2 = -1.45562130224 Factor a perfect square on the left side: (x + -0.0769230769)(x + -0.0769230769) = -1.45562130224 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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