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Simplifying 4x4 + -4x3 + -7x2 + -4x + 4x = 0 Reorder the terms: -4x + 4x + -7x2 + -4x3 + 4x4 = 0 Combine like terms: -4x + 4x = 0 0 + -7x2 + -4x3 + 4x4 = 0 -7x2 + -4x3 + 4x4 = 0 Solving -7x2 + -4x3 + 4x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(-7 + -4x + 4x2) = 0Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(-7 + -4x + 4x2)' equal to zero and attempt to solve: Simplifying -7 + -4x + 4x2 = 0 Solving -7 + -4x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.75 + -1x + x2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + -1x + 1.75 + x2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + -1x + x2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + -1x + x2 = 0 + 1.75 -1x + x2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 -1x + x2 = 1.75 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 1.75 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 1.75 + 0.25 Combine like terms: 1.75 + 0.25 = 2 0.25 + -1x + x2 = 2 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (x + -0.5) equal to 1.414213562 and -1.414213562.Subproblem 1
x + -0.5 = 1.414213562 Simplifying x + -0.5 = 1.414213562 Reorder the terms: -0.5 + x = 1.414213562 Solving -0.5 + x = 1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 1.414213562 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.414213562 + 0.5 x = 1.414213562 + 0.5 Combine like terms: 1.414213562 + 0.5 = 1.914213562 x = 1.914213562 Simplifying x = 1.914213562Subproblem 2
x + -0.5 = -1.414213562 Simplifying x + -0.5 = -1.414213562 Reorder the terms: -0.5 + x = -1.414213562 Solving -0.5 + x = -1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -1.414213562 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.414213562 + 0.5 x = -1.414213562 + 0.5 Combine like terms: -1.414213562 + 0.5 = -0.914213562 x = -0.914213562 Simplifying x = -0.914213562Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.914213562, -0.914213562}Solution
x = {0, 1.914213562, -0.914213562}
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