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Simplifying 0 = -16x2 + 55x + 175 Reorder the terms: 0 = 175 + 55x + -16x2 Solving 0 = 175 + 55x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -175 = -175 -175 + -55x + 16x2 = 175 + 55x + -16x2 + -175 + -55x + 16x2 Reorder the terms: -175 + -55x + 16x2 = 175 + -175 + 55x + -55x + -16x2 + 16x2 Combine like terms: 175 + -175 = 0 -175 + -55x + 16x2 = 0 + 55x + -55x + -16x2 + 16x2 -175 + -55x + 16x2 = 55x + -55x + -16x2 + 16x2 Combine like terms: 55x + -55x = 0 -175 + -55x + 16x2 = 0 + -16x2 + 16x2 -175 + -55x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -175 + -55x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -10.9375 + -3.4375x + x2 = 0 Move the constant term to the right: Add '10.9375' to each side of the equation. -10.9375 + -3.4375x + 10.9375 + x2 = 0 + 10.9375 Reorder the terms: -10.9375 + 10.9375 + -3.4375x + x2 = 0 + 10.9375 Combine like terms: -10.9375 + 10.9375 = 0.0000 0.0000 + -3.4375x + x2 = 0 + 10.9375 -3.4375x + x2 = 0 + 10.9375 Combine like terms: 0 + 10.9375 = 10.9375 -3.4375x + x2 = 10.9375 The x term is -3.4375x. Take half its coefficient (-1.71875). Square it (2.954101563) and add it to both sides. Add '2.954101563' to each side of the equation. -3.4375x + 2.954101563 + x2 = 10.9375 + 2.954101563 Reorder the terms: 2.954101563 + -3.4375x + x2 = 10.9375 + 2.954101563 Combine like terms: 10.9375 + 2.954101563 = 13.891601563 2.954101563 + -3.4375x + x2 = 13.891601563 Factor a perfect square on the left side: (x + -1.71875)(x + -1.71875) = 13.891601563 Calculate the square root of the right side: 3.727143888 Break this problem into two subproblems by setting (x + -1.71875) equal to 3.727143888 and -3.727143888.Subproblem 1
x + -1.71875 = 3.727143888 Simplifying x + -1.71875 = 3.727143888 Reorder the terms: -1.71875 + x = 3.727143888 Solving -1.71875 + x = 3.727143888 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.71875' to each side of the equation. -1.71875 + 1.71875 + x = 3.727143888 + 1.71875 Combine like terms: -1.71875 + 1.71875 = 0.00000 0.00000 + x = 3.727143888 + 1.71875 x = 3.727143888 + 1.71875 Combine like terms: 3.727143888 + 1.71875 = 5.445893888 x = 5.445893888 Simplifying x = 5.445893888Subproblem 2
x + -1.71875 = -3.727143888 Simplifying x + -1.71875 = -3.727143888 Reorder the terms: -1.71875 + x = -3.727143888 Solving -1.71875 + x = -3.727143888 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.71875' to each side of the equation. -1.71875 + 1.71875 + x = -3.727143888 + 1.71875 Combine like terms: -1.71875 + 1.71875 = 0.00000 0.00000 + x = -3.727143888 + 1.71875 x = -3.727143888 + 1.71875 Combine like terms: -3.727143888 + 1.71875 = -2.008393888 x = -2.008393888 Simplifying x = -2.008393888Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.445893888, -2.008393888}
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