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Simplifying 3x3 + -7x2 + -1x = 0 Reorder the terms: -1x + -7x2 + 3x3 = 0 Solving -1x + -7x2 + 3x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-1 + -7x + 3x2) = 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 '(-1 + -7x + 3x2)' equal to zero and attempt to solve: Simplifying -1 + -7x + 3x2 = 0 Solving -1 + -7x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -0.3333333333 + -2.333333333x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + -2.333333333x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + -2.333333333x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + -2.333333333x + x2 = 0 + 0.3333333333 -2.333333333x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 -2.333333333x + x2 = 0.3333333333 The x term is -2.333333333x. Take half its coefficient (-1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. -2.333333333x + 1.361111112 + x2 = 0.3333333333 + 1.361111112 Reorder the terms: 1.361111112 + -2.333333333x + x2 = 0.3333333333 + 1.361111112 Combine like terms: 0.3333333333 + 1.361111112 = 1.6944444453 1.361111112 + -2.333333333x + x2 = 1.6944444453 Factor a perfect square on the left side: (x + -1.166666667)(x + -1.166666667) = 1.6944444453 Calculate the square root of the right side: 1.30170828 Break this problem into two subproblems by setting (x + -1.166666667) equal to 1.30170828 and -1.30170828.Subproblem 1
x + -1.166666667 = 1.30170828 Simplifying x + -1.166666667 = 1.30170828 Reorder the terms: -1.166666667 + x = 1.30170828 Solving -1.166666667 + x = 1.30170828 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + x = 1.30170828 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = 1.30170828 + 1.166666667 x = 1.30170828 + 1.166666667 Combine like terms: 1.30170828 + 1.166666667 = 2.468374947 x = 2.468374947 Simplifying x = 2.468374947Subproblem 2
x + -1.166666667 = -1.30170828 Simplifying x + -1.166666667 = -1.30170828 Reorder the terms: -1.166666667 + x = -1.30170828 Solving -1.166666667 + x = -1.30170828 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + x = -1.30170828 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = -1.30170828 + 1.166666667 x = -1.30170828 + 1.166666667 Combine like terms: -1.30170828 + 1.166666667 = -0.135041613 x = -0.135041613 Simplifying x = -0.135041613Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.468374947, -0.135041613}Solution
x = {0, 2.468374947, -0.135041613}
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