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Simplifying 7x3 + -3x2 + -168x = 0 Reorder the terms: -168x + -3x2 + 7x3 = 0 Solving -168x + -3x2 + 7x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-168 + -3x + 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 '(-168 + -3x + 7x2)' equal to zero and attempt to solve: Simplifying -168 + -3x + 7x2 = 0 Solving -168 + -3x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -24 + -0.4285714286x + x2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + -0.4285714286x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + -0.4285714286x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -0.4285714286x + x2 = 0 + 24 -0.4285714286x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 -0.4285714286x + x2 = 24 The x term is -0.4285714286x. Take half its coefficient (-0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. -0.4285714286x + 0.04591836735 + x2 = 24 + 0.04591836735 Reorder the terms: 0.04591836735 + -0.4285714286x + x2 = 24 + 0.04591836735 Combine like terms: 24 + 0.04591836735 = 24.04591836735 0.04591836735 + -0.4285714286x + x2 = 24.04591836735 Factor a perfect square on the left side: (x + -0.2142857143)(x + -0.2142857143) = 24.04591836735 Calculate the square root of the right side: 4.90366377 Break this problem into two subproblems by setting (x + -0.2142857143) equal to 4.90366377 and -4.90366377.Subproblem 1
x + -0.2142857143 = 4.90366377 Simplifying x + -0.2142857143 = 4.90366377 Reorder the terms: -0.2142857143 + x = 4.90366377 Solving -0.2142857143 + x = 4.90366377 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2142857143' to each side of the equation. -0.2142857143 + 0.2142857143 + x = 4.90366377 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + x = 4.90366377 + 0.2142857143 x = 4.90366377 + 0.2142857143 Combine like terms: 4.90366377 + 0.2142857143 = 5.1179494843 x = 5.1179494843 Simplifying x = 5.1179494843Subproblem 2
x + -0.2142857143 = -4.90366377 Simplifying x + -0.2142857143 = -4.90366377 Reorder the terms: -0.2142857143 + x = -4.90366377 Solving -0.2142857143 + x = -4.90366377 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2142857143' to each side of the equation. -0.2142857143 + 0.2142857143 + x = -4.90366377 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + x = -4.90366377 + 0.2142857143 x = -4.90366377 + 0.2142857143 Combine like terms: -4.90366377 + 0.2142857143 = -4.6893780557 x = -4.6893780557 Simplifying x = -4.6893780557Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.1179494843, -4.6893780557}Solution
x = {0, 5.1179494843, -4.6893780557}
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