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Simplifying x3 + -14x2 + -42x = 0 Reorder the terms: -42x + -14x2 + x3 = 0 Solving -42x + -14x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-42 + -14x + x2) = 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 '(-42 + -14x + x2)' equal to zero and attempt to solve: Simplifying -42 + -14x + x2 = 0 Solving -42 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '42' to each side of the equation. -42 + -14x + 42 + x2 = 0 + 42 Reorder the terms: -42 + 42 + -14x + x2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + -14x + x2 = 0 + 42 -14x + x2 = 0 + 42 Combine like terms: 0 + 42 = 42 -14x + x2 = 42 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = 42 + 49 Reorder the terms: 49 + -14x + x2 = 42 + 49 Combine like terms: 42 + 49 = 91 49 + -14x + x2 = 91 Factor a perfect square on the left side: (x + -7)(x + -7) = 91 Calculate the square root of the right side: 9.539392014 Break this problem into two subproblems by setting (x + -7) equal to 9.539392014 and -9.539392014.Subproblem 1
x + -7 = 9.539392014 Simplifying x + -7 = 9.539392014 Reorder the terms: -7 + x = 9.539392014 Solving -7 + x = 9.539392014 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 9.539392014 + 7 Combine like terms: -7 + 7 = 0 0 + x = 9.539392014 + 7 x = 9.539392014 + 7 Combine like terms: 9.539392014 + 7 = 16.539392014 x = 16.539392014 Simplifying x = 16.539392014Subproblem 2
x + -7 = -9.539392014 Simplifying x + -7 = -9.539392014 Reorder the terms: -7 + x = -9.539392014 Solving -7 + x = -9.539392014 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -9.539392014 + 7 Combine like terms: -7 + 7 = 0 0 + x = -9.539392014 + 7 x = -9.539392014 + 7 Combine like terms: -9.539392014 + 7 = -2.539392014 x = -2.539392014 Simplifying x = -2.539392014Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.539392014, -2.539392014}Solution
x = {0, 16.539392014, -2.539392014}
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