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Simplifying 16x4 + 22x3 + -4x2 = 0 Reorder the terms: -4x2 + 22x3 + 16x4 = 0 Solving -4x2 + 22x3 + 16x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x2'. 2x2(-2 + 11x + 8x2) = 0 Ignore the factor 2.Subproblem 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 '(-2 + 11x + 8x2)' equal to zero and attempt to solve: Simplifying -2 + 11x + 8x2 = 0 Solving -2 + 11x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.25 + 1.375x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + 1.375x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + 1.375x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + 1.375x + x2 = 0 + 0.25 1.375x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 1.375x + x2 = 0.25 The x term is 1.375x. Take half its coefficient (0.6875). Square it (0.47265625) and add it to both sides. Add '0.47265625' to each side of the equation. 1.375x + 0.47265625 + x2 = 0.25 + 0.47265625 Reorder the terms: 0.47265625 + 1.375x + x2 = 0.25 + 0.47265625 Combine like terms: 0.25 + 0.47265625 = 0.72265625 0.47265625 + 1.375x + x2 = 0.72265625 Factor a perfect square on the left side: (x + 0.6875)(x + 0.6875) = 0.72265625 Calculate the square root of the right side: 0.850091907 Break this problem into two subproblems by setting (x + 0.6875) equal to 0.850091907 and -0.850091907.Subproblem 1
x + 0.6875 = 0.850091907 Simplifying x + 0.6875 = 0.850091907 Reorder the terms: 0.6875 + x = 0.850091907 Solving 0.6875 + x = 0.850091907 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6875' to each side of the equation. 0.6875 + -0.6875 + x = 0.850091907 + -0.6875 Combine like terms: 0.6875 + -0.6875 = 0.0000 0.0000 + x = 0.850091907 + -0.6875 x = 0.850091907 + -0.6875 Combine like terms: 0.850091907 + -0.6875 = 0.162591907 x = 0.162591907 Simplifying x = 0.162591907Subproblem 2
x + 0.6875 = -0.850091907 Simplifying x + 0.6875 = -0.850091907 Reorder the terms: 0.6875 + x = -0.850091907 Solving 0.6875 + x = -0.850091907 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6875' to each side of the equation. 0.6875 + -0.6875 + x = -0.850091907 + -0.6875 Combine like terms: 0.6875 + -0.6875 = 0.0000 0.0000 + x = -0.850091907 + -0.6875 x = -0.850091907 + -0.6875 Combine like terms: -0.850091907 + -0.6875 = -1.537591907 x = -1.537591907 Simplifying x = -1.537591907Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.162591907, -1.537591907}Solution
x = {0, 0.162591907, -1.537591907}
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