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Simplifying 14x3 + -12x2 + -48x = 0 Reorder the terms: -48x + -12x2 + 14x3 = 0 Solving -48x + -12x2 + 14x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-24 + -6x + 7x2) = 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 '(-24 + -6x + 7x2)' equal to zero and attempt to solve: Simplifying -24 + -6x + 7x2 = 0 Solving -24 + -6x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -3.428571429 + -0.8571428571x + x2 = 0 Move the constant term to the right: Add '3.428571429' to each side of the equation. -3.428571429 + -0.8571428571x + 3.428571429 + x2 = 0 + 3.428571429 Reorder the terms: -3.428571429 + 3.428571429 + -0.8571428571x + x2 = 0 + 3.428571429 Combine like terms: -3.428571429 + 3.428571429 = 0.000000000 0.000000000 + -0.8571428571x + x2 = 0 + 3.428571429 -0.8571428571x + x2 = 0 + 3.428571429 Combine like terms: 0 + 3.428571429 = 3.428571429 -0.8571428571x + x2 = 3.428571429 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 = 3.428571429 + 0.1836734694 Reorder the terms: 0.1836734694 + -0.8571428571x + x2 = 3.428571429 + 0.1836734694 Combine like terms: 3.428571429 + 0.1836734694 = 3.6122448984 0.1836734694 + -0.8571428571x + x2 = 3.6122448984 Factor a perfect square on the left side: (x + -0.4285714286)(x + -0.4285714286) = 3.6122448984 Calculate the square root of the right side: 1.900590671 Break this problem into two subproblems by setting (x + -0.4285714286) equal to 1.900590671 and -1.900590671.Subproblem 1
x + -0.4285714286 = 1.900590671 Simplifying x + -0.4285714286 = 1.900590671 Reorder the terms: -0.4285714286 + x = 1.900590671 Solving -0.4285714286 + x = 1.900590671 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 = 1.900590671 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = 1.900590671 + 0.4285714286 x = 1.900590671 + 0.4285714286 Combine like terms: 1.900590671 + 0.4285714286 = 2.3291620996 x = 2.3291620996 Simplifying x = 2.3291620996Subproblem 2
x + -0.4285714286 = -1.900590671 Simplifying x + -0.4285714286 = -1.900590671 Reorder the terms: -0.4285714286 + x = -1.900590671 Solving -0.4285714286 + x = -1.900590671 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 = -1.900590671 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = -1.900590671 + 0.4285714286 x = -1.900590671 + 0.4285714286 Combine like terms: -1.900590671 + 0.4285714286 = -1.4720192424 x = -1.4720192424 Simplifying x = -1.4720192424Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.3291620996, -1.4720192424}Solution
x = {0, 2.3291620996, -1.4720192424}
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