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Simplifying -16x2 + 66x + 13 = 44 Reorder the terms: 13 + 66x + -16x2 = 44 Solving 13 + 66x + -16x2 = 44 Solving for variable 'x'. Reorder the terms: 13 + -44 + 66x + -16x2 = 44 + -44 Combine like terms: 13 + -44 = -31 -31 + 66x + -16x2 = 44 + -44 Combine like terms: 44 + -44 = 0 -31 + 66x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 1.9375 + -4.125x + x2 = 0 Move the constant term to the right: Add '-1.9375' to each side of the equation. 1.9375 + -4.125x + -1.9375 + x2 = 0 + -1.9375 Reorder the terms: 1.9375 + -1.9375 + -4.125x + x2 = 0 + -1.9375 Combine like terms: 1.9375 + -1.9375 = 0.0000 0.0000 + -4.125x + x2 = 0 + -1.9375 -4.125x + x2 = 0 + -1.9375 Combine like terms: 0 + -1.9375 = -1.9375 -4.125x + x2 = -1.9375 The x term is -4.125x. Take half its coefficient (-2.0625). Square it (4.25390625) and add it to both sides. Add '4.25390625' to each side of the equation. -4.125x + 4.25390625 + x2 = -1.9375 + 4.25390625 Reorder the terms: 4.25390625 + -4.125x + x2 = -1.9375 + 4.25390625 Combine like terms: -1.9375 + 4.25390625 = 2.31640625 4.25390625 + -4.125x + x2 = 2.31640625 Factor a perfect square on the left side: (x + -2.0625)(x + -2.0625) = 2.31640625 Calculate the square root of the right side: 1.521974458 Break this problem into two subproblems by setting (x + -2.0625) equal to 1.521974458 and -1.521974458.Subproblem 1
x + -2.0625 = 1.521974458 Simplifying x + -2.0625 = 1.521974458 Reorder the terms: -2.0625 + x = 1.521974458 Solving -2.0625 + x = 1.521974458 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.0625' to each side of the equation. -2.0625 + 2.0625 + x = 1.521974458 + 2.0625 Combine like terms: -2.0625 + 2.0625 = 0.0000 0.0000 + x = 1.521974458 + 2.0625 x = 1.521974458 + 2.0625 Combine like terms: 1.521974458 + 2.0625 = 3.584474458 x = 3.584474458 Simplifying x = 3.584474458Subproblem 2
x + -2.0625 = -1.521974458 Simplifying x + -2.0625 = -1.521974458 Reorder the terms: -2.0625 + x = -1.521974458 Solving -2.0625 + x = -1.521974458 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.0625' to each side of the equation. -2.0625 + 2.0625 + x = -1.521974458 + 2.0625 Combine like terms: -2.0625 + 2.0625 = 0.0000 0.0000 + x = -1.521974458 + 2.0625 x = -1.521974458 + 2.0625 Combine like terms: -1.521974458 + 2.0625 = 0.540525542 x = 0.540525542 Simplifying x = 0.540525542Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.584474458, 0.540525542}
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