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Simplifying 7x3 + 18x2 + -30x = 0 Reorder the terms: -30x + 18x2 + 7x3 = 0 Solving -30x + 18x2 + 7x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-30 + 18x + 7x2) = 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 '(-30 + 18x + 7x2)' equal to zero and attempt to solve: Simplifying -30 + 18x + 7x2 = 0 Solving -30 + 18x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -4.285714286 + 2.571428571x + x2 = 0 Move the constant term to the right: Add '4.285714286' to each side of the equation. -4.285714286 + 2.571428571x + 4.285714286 + x2 = 0 + 4.285714286 Reorder the terms: -4.285714286 + 4.285714286 + 2.571428571x + x2 = 0 + 4.285714286 Combine like terms: -4.285714286 + 4.285714286 = 0.000000000 0.000000000 + 2.571428571x + x2 = 0 + 4.285714286 2.571428571x + x2 = 0 + 4.285714286 Combine like terms: 0 + 4.285714286 = 4.285714286 2.571428571x + x2 = 4.285714286 The x term is 2.571428571x. Take half its coefficient (1.285714286). Square it (1.653061225) and add it to both sides. Add '1.653061225' to each side of the equation. 2.571428571x + 1.653061225 + x2 = 4.285714286 + 1.653061225 Reorder the terms: 1.653061225 + 2.571428571x + x2 = 4.285714286 + 1.653061225 Combine like terms: 4.285714286 + 1.653061225 = 5.938775511 1.653061225 + 2.571428571x + x2 = 5.938775511 Factor a perfect square on the left side: (x + 1.285714286)(x + 1.285714286) = 5.938775511 Calculate the square root of the right side: 2.436960301 Break this problem into two subproblems by setting (x + 1.285714286) equal to 2.436960301 and -2.436960301.Subproblem 1
x + 1.285714286 = 2.436960301 Simplifying x + 1.285714286 = 2.436960301 Reorder the terms: 1.285714286 + x = 2.436960301 Solving 1.285714286 + x = 2.436960301 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.285714286' to each side of the equation. 1.285714286 + -1.285714286 + x = 2.436960301 + -1.285714286 Combine like terms: 1.285714286 + -1.285714286 = 0.000000000 0.000000000 + x = 2.436960301 + -1.285714286 x = 2.436960301 + -1.285714286 Combine like terms: 2.436960301 + -1.285714286 = 1.151246015 x = 1.151246015 Simplifying x = 1.151246015Subproblem 2
x + 1.285714286 = -2.436960301 Simplifying x + 1.285714286 = -2.436960301 Reorder the terms: 1.285714286 + x = -2.436960301 Solving 1.285714286 + x = -2.436960301 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.285714286' to each side of the equation. 1.285714286 + -1.285714286 + x = -2.436960301 + -1.285714286 Combine like terms: 1.285714286 + -1.285714286 = 0.000000000 0.000000000 + x = -2.436960301 + -1.285714286 x = -2.436960301 + -1.285714286 Combine like terms: -2.436960301 + -1.285714286 = -3.722674587 x = -3.722674587 Simplifying x = -3.722674587Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.151246015, -3.722674587}Solution
x = {0, 1.151246015, -3.722674587}
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