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Simplifying (2x3) + (4x2) + -7x = 0 Reorder the terms: -7x + (4x2) + (2x3) = 0 Solving -7x + (4x2) + (2x3) = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-7 + (4x) + (2x2)) = 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 '(-7 + (4x) + (2x2))' equal to zero and attempt to solve: Simplifying -7 + (4x) + (2x2) = 0 Solving -7 + (4x) + (2x2) = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.5 + (2x) + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + (2x) + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + (2x) + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + (2x) + x2 = 0 + 3.5 (2x) + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 (2x) + x2 = 3.5 The x term is (2x). Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. (2x) + 1 + x2 = 3.5 + 1 Reorder the terms: 1 + (2x) + x2 = 3.5 + 1 Combine like terms: 3.5 + 1 = 4.5 1 + (2x) + x2 = 4.5 Factor a perfect square on the left side: ((x) + 1)((x) + 1) = 4.5 Calculate the square root of the right side: 2.121320344 Break this problem into two subproblems by setting ((x) + 1) equal to 2.121320344 and -2.121320344.Subproblem 1
(x) + 1 = 2.121320344 Simplifying (x) + 1 = 2.121320344 x + 1 = 2.121320344 Reorder the terms: 1 + x = 2.121320344 Solving 1 + x = 2.121320344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 2.121320344 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.121320344 + -1 x = 2.121320344 + -1 Combine like terms: 2.121320344 + -1 = 1.121320344 x = 1.121320344 Simplifying x = 1.121320344Subproblem 2
(x) + 1 = -2.121320344 Simplifying (x) + 1 = -2.121320344 x + 1 = -2.121320344 Reorder the terms: 1 + x = -2.121320344 Solving 1 + x = -2.121320344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -2.121320344 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.121320344 + -1 x = -2.121320344 + -1 Combine like terms: -2.121320344 + -1 = -3.121320344 x = -3.121320344 Simplifying x = -3.121320344Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.121320344, -3.121320344}Solution
x = {0, 1.121320344, -3.121320344}
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