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Simplifying 3x3 + 23x2 + -14x = 0 Reorder the terms: -14x + 23x2 + 3x3 = 0 Solving -14x + 23x2 + 3x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-14 + 23x + 3x2) = 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 '(-14 + 23x + 3x2)' equal to zero and attempt to solve: Simplifying -14 + 23x + 3x2 = 0 Solving -14 + 23x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -4.666666667 + 7.666666667x + x2 = 0 Move the constant term to the right: Add '4.666666667' to each side of the equation. -4.666666667 + 7.666666667x + 4.666666667 + x2 = 0 + 4.666666667 Reorder the terms: -4.666666667 + 4.666666667 + 7.666666667x + x2 = 0 + 4.666666667 Combine like terms: -4.666666667 + 4.666666667 = 0.000000000 0.000000000 + 7.666666667x + x2 = 0 + 4.666666667 7.666666667x + x2 = 0 + 4.666666667 Combine like terms: 0 + 4.666666667 = 4.666666667 7.666666667x + x2 = 4.666666667 The x term is 7.666666667x. Take half its coefficient (3.833333334). Square it (14.69444445) and add it to both sides. Add '14.69444445' to each side of the equation. 7.666666667x + 14.69444445 + x2 = 4.666666667 + 14.69444445 Reorder the terms: 14.69444445 + 7.666666667x + x2 = 4.666666667 + 14.69444445 Combine like terms: 4.666666667 + 14.69444445 = 19.361111117 14.69444445 + 7.666666667x + x2 = 19.361111117 Factor a perfect square on the left side: (x + 3.833333334)(x + 3.833333334) = 19.361111117 Calculate the square root of the right side: 4.400126261 Break this problem into two subproblems by setting (x + 3.833333334) equal to 4.400126261 and -4.400126261.Subproblem 1
x + 3.833333334 = 4.400126261 Simplifying x + 3.833333334 = 4.400126261 Reorder the terms: 3.833333334 + x = 4.400126261 Solving 3.833333334 + x = 4.400126261 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.833333334' to each side of the equation. 3.833333334 + -3.833333334 + x = 4.400126261 + -3.833333334 Combine like terms: 3.833333334 + -3.833333334 = 0.000000000 0.000000000 + x = 4.400126261 + -3.833333334 x = 4.400126261 + -3.833333334 Combine like terms: 4.400126261 + -3.833333334 = 0.566792927 x = 0.566792927 Simplifying x = 0.566792927Subproblem 2
x + 3.833333334 = -4.400126261 Simplifying x + 3.833333334 = -4.400126261 Reorder the terms: 3.833333334 + x = -4.400126261 Solving 3.833333334 + x = -4.400126261 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.833333334' to each side of the equation. 3.833333334 + -3.833333334 + x = -4.400126261 + -3.833333334 Combine like terms: 3.833333334 + -3.833333334 = 0.000000000 0.000000000 + x = -4.400126261 + -3.833333334 x = -4.400126261 + -3.833333334 Combine like terms: -4.400126261 + -3.833333334 = -8.233459595 x = -8.233459595 Simplifying x = -8.233459595Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.566792927, -8.233459595}Solution
x = {0, 0.566792927, -8.233459595}
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