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Simplifying 6x3 + -61x2 = 10x Reorder the terms: -61x2 + 6x3 = 10x Solving -61x2 + 6x3 = 10x Solving for variable 'x'. Reorder the terms: -10x + -61x2 + 6x3 = 10x + -10x Combine like terms: 10x + -10x = 0 -10x + -61x2 + 6x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-10 + -61x + 6x2) = 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 '(-10 + -61x + 6x2)' equal to zero and attempt to solve: Simplifying -10 + -61x + 6x2 = 0 Solving -10 + -61x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1.666666667 + -10.16666667x + x2 = 0 Move the constant term to the right: Add '1.666666667' to each side of the equation. -1.666666667 + -10.16666667x + 1.666666667 + x2 = 0 + 1.666666667 Reorder the terms: -1.666666667 + 1.666666667 + -10.16666667x + x2 = 0 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + -10.16666667x + x2 = 0 + 1.666666667 -10.16666667x + x2 = 0 + 1.666666667 Combine like terms: 0 + 1.666666667 = 1.666666667 -10.16666667x + x2 = 1.666666667 The x term is -10.16666667x. Take half its coefficient (-5.083333335). Square it (25.84027779) and add it to both sides. Add '25.84027779' to each side of the equation. -10.16666667x + 25.84027779 + x2 = 1.666666667 + 25.84027779 Reorder the terms: 25.84027779 + -10.16666667x + x2 = 1.666666667 + 25.84027779 Combine like terms: 1.666666667 + 25.84027779 = 27.506944457 25.84027779 + -10.16666667x + x2 = 27.506944457 Factor a perfect square on the left side: (x + -5.083333335)(x + -5.083333335) = 27.506944457 Calculate the square root of the right side: 5.244706327 Break this problem into two subproblems by setting (x + -5.083333335) equal to 5.244706327 and -5.244706327.Subproblem 1
x + -5.083333335 = 5.244706327 Simplifying x + -5.083333335 = 5.244706327 Reorder the terms: -5.083333335 + x = 5.244706327 Solving -5.083333335 + x = 5.244706327 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.083333335' to each side of the equation. -5.083333335 + 5.083333335 + x = 5.244706327 + 5.083333335 Combine like terms: -5.083333335 + 5.083333335 = 0.000000000 0.000000000 + x = 5.244706327 + 5.083333335 x = 5.244706327 + 5.083333335 Combine like terms: 5.244706327 + 5.083333335 = 10.328039662 x = 10.328039662 Simplifying x = 10.328039662Subproblem 2
x + -5.083333335 = -5.244706327 Simplifying x + -5.083333335 = -5.244706327 Reorder the terms: -5.083333335 + x = -5.244706327 Solving -5.083333335 + x = -5.244706327 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.083333335' to each side of the equation. -5.083333335 + 5.083333335 + x = -5.244706327 + 5.083333335 Combine like terms: -5.083333335 + 5.083333335 = 0.000000000 0.000000000 + x = -5.244706327 + 5.083333335 x = -5.244706327 + 5.083333335 Combine like terms: -5.244706327 + 5.083333335 = -0.161372992 x = -0.161372992 Simplifying x = -0.161372992Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.328039662, -0.161372992}Solution
x = {0, 10.328039662, -0.161372992}
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