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Simplifying x3 + 4x2 + -7x = 0 Reorder the terms: -7x + 4x2 + x3 = 0 Solving -7x + 4x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-7 + 4x + 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 '(-7 + 4x + x2)' equal to zero and attempt to solve: Simplifying -7 + 4x + x2 = 0 Solving -7 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + 4x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + 4x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 4x + x2 = 0 + 7 4x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 4x + x2 = 7 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 7 + 4 Reorder the terms: 4 + 4x + x2 = 7 + 4 Combine like terms: 7 + 4 = 11 4 + 4x + x2 = 11 Factor a perfect square on the left side: (x + 2)(x + 2) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (x + 2) equal to 3.31662479 and -3.31662479.Subproblem 1
x + 2 = 3.31662479 Simplifying x + 2 = 3.31662479 Reorder the terms: 2 + x = 3.31662479 Solving 2 + x = 3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 3.31662479 + -2 Combine like terms: 2 + -2 = 0 0 + x = 3.31662479 + -2 x = 3.31662479 + -2 Combine like terms: 3.31662479 + -2 = 1.31662479 x = 1.31662479 Simplifying x = 1.31662479Subproblem 2
x + 2 = -3.31662479 Simplifying x + 2 = -3.31662479 Reorder the terms: 2 + x = -3.31662479 Solving 2 + x = -3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -3.31662479 + -2 Combine like terms: 2 + -2 = 0 0 + x = -3.31662479 + -2 x = -3.31662479 + -2 Combine like terms: -3.31662479 + -2 = -5.31662479 x = -5.31662479 Simplifying x = -5.31662479Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.31662479, -5.31662479}Solution
x = {0, 1.31662479, -5.31662479}
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