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Simplifying -16x2 + 44x + 4 = 0 Reorder the terms: 4 + 44x + -16x2 = 0 Solving 4 + 44x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(1 + 11x + -4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + 11x + -4x2)' equal to zero and attempt to solve: Simplifying 1 + 11x + -4x2 = 0 Solving 1 + 11x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -0.25 + -2.75x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -2.75x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -2.75x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -2.75x + x2 = 0 + 0.25 -2.75x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -2.75x + x2 = 0.25 The x term is -2.75x. Take half its coefficient (-1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. -2.75x + 1.890625 + x2 = 0.25 + 1.890625 Reorder the terms: 1.890625 + -2.75x + x2 = 0.25 + 1.890625 Combine like terms: 0.25 + 1.890625 = 2.140625 1.890625 + -2.75x + x2 = 2.140625 Factor a perfect square on the left side: (x + -1.375)(x + -1.375) = 2.140625 Calculate the square root of the right side: 1.463087489 Break this problem into two subproblems by setting (x + -1.375) equal to 1.463087489 and -1.463087489.Subproblem 1
x + -1.375 = 1.463087489 Simplifying x + -1.375 = 1.463087489 Reorder the terms: -1.375 + x = 1.463087489 Solving -1.375 + x = 1.463087489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = 1.463087489 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = 1.463087489 + 1.375 x = 1.463087489 + 1.375 Combine like terms: 1.463087489 + 1.375 = 2.838087489 x = 2.838087489 Simplifying x = 2.838087489Subproblem 2
x + -1.375 = -1.463087489 Simplifying x + -1.375 = -1.463087489 Reorder the terms: -1.375 + x = -1.463087489 Solving -1.375 + x = -1.463087489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = -1.463087489 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = -1.463087489 + 1.375 x = -1.463087489 + 1.375 Combine like terms: -1.463087489 + 1.375 = -0.088087489 x = -0.088087489 Simplifying x = -0.088087489Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.838087489, -0.088087489}Solution
x = {2.838087489, -0.088087489}
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