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Simplifying 4x4 + -7x3 + -1x2 = 0 Reorder the terms: -1x2 + -7x3 + 4x4 = 0 Solving -1x2 + -7x3 + 4x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(-1 + -7x + 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 '(-1 + -7x + 4x2)' equal to zero and attempt to solve: Simplifying -1 + -7x + 4x2 = 0 Solving -1 + -7x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.25 + -1.75x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -1.75x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -1.75x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -1.75x + x2 = 0 + 0.25 -1.75x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -1.75x + x2 = 0.25 The x term is -1.75x. Take half its coefficient (-0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. -1.75x + 0.765625 + x2 = 0.25 + 0.765625 Reorder the terms: 0.765625 + -1.75x + x2 = 0.25 + 0.765625 Combine like terms: 0.25 + 0.765625 = 1.015625 0.765625 + -1.75x + x2 = 1.015625 Factor a perfect square on the left side: (x + -0.875)(x + -0.875) = 1.015625 Calculate the square root of the right side: 1.007782219 Break this problem into two subproblems by setting (x + -0.875) equal to 1.007782219 and -1.007782219.Subproblem 1
x + -0.875 = 1.007782219 Simplifying x + -0.875 = 1.007782219 Reorder the terms: -0.875 + x = 1.007782219 Solving -0.875 + x = 1.007782219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x = 1.007782219 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = 1.007782219 + 0.875 x = 1.007782219 + 0.875 Combine like terms: 1.007782219 + 0.875 = 1.882782219 x = 1.882782219 Simplifying x = 1.882782219Subproblem 2
x + -0.875 = -1.007782219 Simplifying x + -0.875 = -1.007782219 Reorder the terms: -0.875 + x = -1.007782219 Solving -0.875 + x = -1.007782219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x = -1.007782219 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = -1.007782219 + 0.875 x = -1.007782219 + 0.875 Combine like terms: -1.007782219 + 0.875 = -0.132782219 x = -0.132782219 Simplifying x = -0.132782219Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.882782219, -0.132782219}Solution
x = {0, 1.882782219, -0.132782219}
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