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Simplifying 70x3 + 60x2 + 12x = 0 Reorder the terms: 12x + 60x2 + 70x3 = 0 Solving 12x + 60x2 + 70x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(6 + 30x + 35x2) = 0 Ignore the factor 2.Subproblem 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 '(6 + 30x + 35x2)' equal to zero and attempt to solve: Simplifying 6 + 30x + 35x2 = 0 Solving 6 + 30x + 35x2 = 0 Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. 0.1714285714 + 0.8571428571x + x2 = 0 Move the constant term to the right: Add '-0.1714285714' to each side of the equation. 0.1714285714 + 0.8571428571x + -0.1714285714 + x2 = 0 + -0.1714285714 Reorder the terms: 0.1714285714 + -0.1714285714 + 0.8571428571x + x2 = 0 + -0.1714285714 Combine like terms: 0.1714285714 + -0.1714285714 = 0.0000000000 0.0000000000 + 0.8571428571x + x2 = 0 + -0.1714285714 0.8571428571x + x2 = 0 + -0.1714285714 Combine like terms: 0 + -0.1714285714 = -0.1714285714 0.8571428571x + x2 = -0.1714285714 The x term is 0.8571428571x. Take half its coefficient (0.4285714286). Square it (0.1836734694) and add it to both sides. Add '0.1836734694' to each side of the equation. 0.8571428571x + 0.1836734694 + x2 = -0.1714285714 + 0.1836734694 Reorder the terms: 0.1836734694 + 0.8571428571x + x2 = -0.1714285714 + 0.1836734694 Combine like terms: -0.1714285714 + 0.1836734694 = 0.012244898 0.1836734694 + 0.8571428571x + x2 = 0.012244898 Factor a perfect square on the left side: (x + 0.4285714286)(x + 0.4285714286) = 0.012244898 Calculate the square root of the right side: 0.110656667 Break this problem into two subproblems by setting (x + 0.4285714286) equal to 0.110656667 and -0.110656667.Subproblem 1
x + 0.4285714286 = 0.110656667 Simplifying x + 0.4285714286 = 0.110656667 Reorder the terms: 0.4285714286 + x = 0.110656667 Solving 0.4285714286 + x = 0.110656667 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4285714286' to each side of the equation. 0.4285714286 + -0.4285714286 + x = 0.110656667 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + x = 0.110656667 + -0.4285714286 x = 0.110656667 + -0.4285714286 Combine like terms: 0.110656667 + -0.4285714286 = -0.3179147616 x = -0.3179147616 Simplifying x = -0.3179147616Subproblem 2
x + 0.4285714286 = -0.110656667 Simplifying x + 0.4285714286 = -0.110656667 Reorder the terms: 0.4285714286 + x = -0.110656667 Solving 0.4285714286 + x = -0.110656667 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4285714286' to each side of the equation. 0.4285714286 + -0.4285714286 + x = -0.110656667 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + x = -0.110656667 + -0.4285714286 x = -0.110656667 + -0.4285714286 Combine like terms: -0.110656667 + -0.4285714286 = -0.5392280956 x = -0.5392280956 Simplifying x = -0.5392280956Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.3179147616, -0.5392280956}Solution
x = {0, -0.3179147616, -0.5392280956}
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