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Simplifying 16x2 + -54x + -16 = 0 Reorder the terms: -16 + -54x + 16x2 = 0 Solving -16 + -54x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + -27x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + -27x + 8x2)' equal to zero and attempt to solve: Simplifying -8 + -27x + 8x2 = 0 Solving -8 + -27x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1 + -3.375x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -3.375x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -3.375x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3.375x + x2 = 0 + 1 -3.375x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -3.375x + x2 = 1 The x term is -3.375x. Take half its coefficient (-1.6875). Square it (2.84765625) and add it to both sides. Add '2.84765625' to each side of the equation. -3.375x + 2.84765625 + x2 = 1 + 2.84765625 Reorder the terms: 2.84765625 + -3.375x + x2 = 1 + 2.84765625 Combine like terms: 1 + 2.84765625 = 3.84765625 2.84765625 + -3.375x + x2 = 3.84765625 Factor a perfect square on the left side: (x + -1.6875)(x + -1.6875) = 3.84765625 Calculate the square root of the right side: 1.961544353 Break this problem into two subproblems by setting (x + -1.6875) equal to 1.961544353 and -1.961544353.Subproblem 1
x + -1.6875 = 1.961544353 Simplifying x + -1.6875 = 1.961544353 Reorder the terms: -1.6875 + x = 1.961544353 Solving -1.6875 + x = 1.961544353 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6875' to each side of the equation. -1.6875 + 1.6875 + x = 1.961544353 + 1.6875 Combine like terms: -1.6875 + 1.6875 = 0.0000 0.0000 + x = 1.961544353 + 1.6875 x = 1.961544353 + 1.6875 Combine like terms: 1.961544353 + 1.6875 = 3.649044353 x = 3.649044353 Simplifying x = 3.649044353Subproblem 2
x + -1.6875 = -1.961544353 Simplifying x + -1.6875 = -1.961544353 Reorder the terms: -1.6875 + x = -1.961544353 Solving -1.6875 + x = -1.961544353 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6875' to each side of the equation. -1.6875 + 1.6875 + x = -1.961544353 + 1.6875 Combine like terms: -1.6875 + 1.6875 = 0.0000 0.0000 + x = -1.961544353 + 1.6875 x = -1.961544353 + 1.6875 Combine like terms: -1.961544353 + 1.6875 = -0.274044353 x = -0.274044353 Simplifying x = -0.274044353Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.649044353, -0.274044353}Solution
x = {3.649044353, -0.274044353}
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