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Simplifying 0 = -16x2 + 49x + 3 Reorder the terms: 0 = 3 + 49x + -16x2 Solving 0 = 3 + 49x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -3 = -3 -3 + -49x + 16x2 = 3 + 49x + -16x2 + -3 + -49x + 16x2 Reorder the terms: -3 + -49x + 16x2 = 3 + -3 + 49x + -49x + -16x2 + 16x2 Combine like terms: 3 + -3 = 0 -3 + -49x + 16x2 = 0 + 49x + -49x + -16x2 + 16x2 -3 + -49x + 16x2 = 49x + -49x + -16x2 + 16x2 Combine like terms: 49x + -49x = 0 -3 + -49x + 16x2 = 0 + -16x2 + 16x2 -3 + -49x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -3 + -49x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.1875 + -3.0625x + x2 = 0 Move the constant term to the right: Add '0.1875' to each side of the equation. -0.1875 + -3.0625x + 0.1875 + x2 = 0 + 0.1875 Reorder the terms: -0.1875 + 0.1875 + -3.0625x + x2 = 0 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + -3.0625x + x2 = 0 + 0.1875 -3.0625x + x2 = 0 + 0.1875 Combine like terms: 0 + 0.1875 = 0.1875 -3.0625x + x2 = 0.1875 The x term is -3.0625x. Take half its coefficient (-1.53125). Square it (2.344726563) and add it to both sides. Add '2.344726563' to each side of the equation. -3.0625x + 2.344726563 + x2 = 0.1875 + 2.344726563 Reorder the terms: 2.344726563 + -3.0625x + x2 = 0.1875 + 2.344726563 Combine like terms: 0.1875 + 2.344726563 = 2.532226563 2.344726563 + -3.0625x + x2 = 2.532226563 Factor a perfect square on the left side: (x + -1.53125)(x + -1.53125) = 2.532226563 Calculate the square root of the right side: 1.591297132 Break this problem into two subproblems by setting (x + -1.53125) equal to 1.591297132 and -1.591297132.Subproblem 1
x + -1.53125 = 1.591297132 Simplifying x + -1.53125 = 1.591297132 Reorder the terms: -1.53125 + x = 1.591297132 Solving -1.53125 + x = 1.591297132 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.53125' to each side of the equation. -1.53125 + 1.53125 + x = 1.591297132 + 1.53125 Combine like terms: -1.53125 + 1.53125 = 0.00000 0.00000 + x = 1.591297132 + 1.53125 x = 1.591297132 + 1.53125 Combine like terms: 1.591297132 + 1.53125 = 3.122547132 x = 3.122547132 Simplifying x = 3.122547132Subproblem 2
x + -1.53125 = -1.591297132 Simplifying x + -1.53125 = -1.591297132 Reorder the terms: -1.53125 + x = -1.591297132 Solving -1.53125 + x = -1.591297132 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.53125' to each side of the equation. -1.53125 + 1.53125 + x = -1.591297132 + 1.53125 Combine like terms: -1.53125 + 1.53125 = 0.00000 0.00000 + x = -1.591297132 + 1.53125 x = -1.591297132 + 1.53125 Combine like terms: -1.591297132 + 1.53125 = -0.060047132 x = -0.060047132 Simplifying x = -0.060047132Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.122547132, -0.060047132}
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