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Simplifying 63x = 16x2 + 6 Reorder the terms: 63x = 6 + 16x2 Solving 63x = 6 + 16x2 Solving for variable 'x'. Reorder the terms: -6 + 63x + -16x2 = 6 + 16x2 + -6 + -16x2 Reorder the terms: -6 + 63x + -16x2 = 6 + -6 + 16x2 + -16x2 Combine like terms: 6 + -6 = 0 -6 + 63x + -16x2 = 0 + 16x2 + -16x2 -6 + 63x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 -6 + 63x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 0.375 + -3.9375x + x2 = 0 Move the constant term to the right: Add '-0.375' to each side of the equation. 0.375 + -3.9375x + -0.375 + x2 = 0 + -0.375 Reorder the terms: 0.375 + -0.375 + -3.9375x + x2 = 0 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + -3.9375x + x2 = 0 + -0.375 -3.9375x + x2 = 0 + -0.375 Combine like terms: 0 + -0.375 = -0.375 -3.9375x + x2 = -0.375 The x term is -3.9375x. Take half its coefficient (-1.96875). Square it (3.875976563) and add it to both sides. Add '3.875976563' to each side of the equation. -3.9375x + 3.875976563 + x2 = -0.375 + 3.875976563 Reorder the terms: 3.875976563 + -3.9375x + x2 = -0.375 + 3.875976563 Combine like terms: -0.375 + 3.875976563 = 3.500976563 3.875976563 + -3.9375x + x2 = 3.500976563 Factor a perfect square on the left side: (x + -1.96875)(x + -1.96875) = 3.500976563 Calculate the square root of the right side: 1.871089673 Break this problem into two subproblems by setting (x + -1.96875) equal to 1.871089673 and -1.871089673.Subproblem 1
x + -1.96875 = 1.871089673 Simplifying x + -1.96875 = 1.871089673 Reorder the terms: -1.96875 + x = 1.871089673 Solving -1.96875 + x = 1.871089673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.96875' to each side of the equation. -1.96875 + 1.96875 + x = 1.871089673 + 1.96875 Combine like terms: -1.96875 + 1.96875 = 0.00000 0.00000 + x = 1.871089673 + 1.96875 x = 1.871089673 + 1.96875 Combine like terms: 1.871089673 + 1.96875 = 3.839839673 x = 3.839839673 Simplifying x = 3.839839673Subproblem 2
x + -1.96875 = -1.871089673 Simplifying x + -1.96875 = -1.871089673 Reorder the terms: -1.96875 + x = -1.871089673 Solving -1.96875 + x = -1.871089673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.96875' to each side of the equation. -1.96875 + 1.96875 + x = -1.871089673 + 1.96875 Combine like terms: -1.96875 + 1.96875 = 0.00000 0.00000 + x = -1.871089673 + 1.96875 x = -1.871089673 + 1.96875 Combine like terms: -1.871089673 + 1.96875 = 0.097660327 x = 0.097660327 Simplifying x = 0.097660327Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.839839673, 0.097660327}
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