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Simplifying 12x3 + -25x2 + -40x = 0 Reorder the terms: -40x + -25x2 + 12x3 = 0 Solving -40x + -25x2 + 12x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-40 + -25x + 12x2) = 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 '(-40 + -25x + 12x2)' equal to zero and attempt to solve: Simplifying -40 + -25x + 12x2 = 0 Solving -40 + -25x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -3.333333333 + -2.083333333x + x2 = 0 Move the constant term to the right: Add '3.333333333' to each side of the equation. -3.333333333 + -2.083333333x + 3.333333333 + x2 = 0 + 3.333333333 Reorder the terms: -3.333333333 + 3.333333333 + -2.083333333x + x2 = 0 + 3.333333333 Combine like terms: -3.333333333 + 3.333333333 = 0.000000000 0.000000000 + -2.083333333x + x2 = 0 + 3.333333333 -2.083333333x + x2 = 0 + 3.333333333 Combine like terms: 0 + 3.333333333 = 3.333333333 -2.083333333x + x2 = 3.333333333 The x term is -2.083333333x. Take half its coefficient (-1.041666667). Square it (1.085069445) and add it to both sides. Add '1.085069445' to each side of the equation. -2.083333333x + 1.085069445 + x2 = 3.333333333 + 1.085069445 Reorder the terms: 1.085069445 + -2.083333333x + x2 = 3.333333333 + 1.085069445 Combine like terms: 3.333333333 + 1.085069445 = 4.418402778 1.085069445 + -2.083333333x + x2 = 4.418402778 Factor a perfect square on the left side: (x + -1.041666667)(x + -1.041666667) = 4.418402778 Calculate the square root of the right side: 2.101999709 Break this problem into two subproblems by setting (x + -1.041666667) equal to 2.101999709 and -2.101999709.Subproblem 1
x + -1.041666667 = 2.101999709 Simplifying x + -1.041666667 = 2.101999709 Reorder the terms: -1.041666667 + x = 2.101999709 Solving -1.041666667 + x = 2.101999709 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.041666667' to each side of the equation. -1.041666667 + 1.041666667 + x = 2.101999709 + 1.041666667 Combine like terms: -1.041666667 + 1.041666667 = 0.000000000 0.000000000 + x = 2.101999709 + 1.041666667 x = 2.101999709 + 1.041666667 Combine like terms: 2.101999709 + 1.041666667 = 3.143666376 x = 3.143666376 Simplifying x = 3.143666376Subproblem 2
x + -1.041666667 = -2.101999709 Simplifying x + -1.041666667 = -2.101999709 Reorder the terms: -1.041666667 + x = -2.101999709 Solving -1.041666667 + x = -2.101999709 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.041666667' to each side of the equation. -1.041666667 + 1.041666667 + x = -2.101999709 + 1.041666667 Combine like terms: -1.041666667 + 1.041666667 = 0.000000000 0.000000000 + x = -2.101999709 + 1.041666667 x = -2.101999709 + 1.041666667 Combine like terms: -2.101999709 + 1.041666667 = -1.060333042 x = -1.060333042 Simplifying x = -1.060333042Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.143666376, -1.060333042}Solution
x = {0, 3.143666376, -1.060333042}
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