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Simplifying 16x2 + -55x + -62 = 0 Reorder the terms: -62 + -55x + 16x2 = 0 Solving -62 + -55x + 16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -3.875 + -3.4375x + x2 = 0 Move the constant term to the right: Add '3.875' to each side of the equation. -3.875 + -3.4375x + 3.875 + x2 = 0 + 3.875 Reorder the terms: -3.875 + 3.875 + -3.4375x + x2 = 0 + 3.875 Combine like terms: -3.875 + 3.875 = 0.000 0.000 + -3.4375x + x2 = 0 + 3.875 -3.4375x + x2 = 0 + 3.875 Combine like terms: 0 + 3.875 = 3.875 -3.4375x + x2 = 3.875 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 = 3.875 + 2.954101563 Reorder the terms: 2.954101563 + -3.4375x + x2 = 3.875 + 2.954101563 Combine like terms: 3.875 + 2.954101563 = 6.829101563 2.954101563 + -3.4375x + x2 = 6.829101563 Factor a perfect square on the left side: (x + -1.71875)(x + -1.71875) = 6.829101563 Calculate the square root of the right side: 2.613254975 Break this problem into two subproblems by setting (x + -1.71875) equal to 2.613254975 and -2.613254975.Subproblem 1
x + -1.71875 = 2.613254975 Simplifying x + -1.71875 = 2.613254975 Reorder the terms: -1.71875 + x = 2.613254975 Solving -1.71875 + x = 2.613254975 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 = 2.613254975 + 1.71875 Combine like terms: -1.71875 + 1.71875 = 0.00000 0.00000 + x = 2.613254975 + 1.71875 x = 2.613254975 + 1.71875 Combine like terms: 2.613254975 + 1.71875 = 4.332004975 x = 4.332004975 Simplifying x = 4.332004975Subproblem 2
x + -1.71875 = -2.613254975 Simplifying x + -1.71875 = -2.613254975 Reorder the terms: -1.71875 + x = -2.613254975 Solving -1.71875 + x = -2.613254975 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 = -2.613254975 + 1.71875 Combine like terms: -1.71875 + 1.71875 = 0.00000 0.00000 + x = -2.613254975 + 1.71875 x = -2.613254975 + 1.71875 Combine like terms: -2.613254975 + 1.71875 = -0.894504975 x = -0.894504975 Simplifying x = -0.894504975Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.332004975, -0.894504975}
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