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Simplifying 16x2 + 62x + 49 = 0 Reorder the terms: 49 + 62x + 16x2 = 0 Solving 49 + 62x + 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'. 3.0625 + 3.875x + x2 = 0 Move the constant term to the right: Add '-3.0625' to each side of the equation. 3.0625 + 3.875x + -3.0625 + x2 = 0 + -3.0625 Reorder the terms: 3.0625 + -3.0625 + 3.875x + x2 = 0 + -3.0625 Combine like terms: 3.0625 + -3.0625 = 0.0000 0.0000 + 3.875x + x2 = 0 + -3.0625 3.875x + x2 = 0 + -3.0625 Combine like terms: 0 + -3.0625 = -3.0625 3.875x + x2 = -3.0625 The x term is 3.875x. Take half its coefficient (1.9375). Square it (3.75390625) and add it to both sides. Add '3.75390625' to each side of the equation. 3.875x + 3.75390625 + x2 = -3.0625 + 3.75390625 Reorder the terms: 3.75390625 + 3.875x + x2 = -3.0625 + 3.75390625 Combine like terms: -3.0625 + 3.75390625 = 0.69140625 3.75390625 + 3.875x + x2 = 0.69140625 Factor a perfect square on the left side: (x + 1.9375)(x + 1.9375) = 0.69140625 Calculate the square root of the right side: 0.831508418 Break this problem into two subproblems by setting (x + 1.9375) equal to 0.831508418 and -0.831508418.Subproblem 1
x + 1.9375 = 0.831508418 Simplifying x + 1.9375 = 0.831508418 Reorder the terms: 1.9375 + x = 0.831508418 Solving 1.9375 + x = 0.831508418 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.9375' to each side of the equation. 1.9375 + -1.9375 + x = 0.831508418 + -1.9375 Combine like terms: 1.9375 + -1.9375 = 0.0000 0.0000 + x = 0.831508418 + -1.9375 x = 0.831508418 + -1.9375 Combine like terms: 0.831508418 + -1.9375 = -1.105991582 x = -1.105991582 Simplifying x = -1.105991582Subproblem 2
x + 1.9375 = -0.831508418 Simplifying x + 1.9375 = -0.831508418 Reorder the terms: 1.9375 + x = -0.831508418 Solving 1.9375 + x = -0.831508418 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.9375' to each side of the equation. 1.9375 + -1.9375 + x = -0.831508418 + -1.9375 Combine like terms: 1.9375 + -1.9375 = 0.0000 0.0000 + x = -0.831508418 + -1.9375 x = -0.831508418 + -1.9375 Combine like terms: -0.831508418 + -1.9375 = -2.769008418 x = -2.769008418 Simplifying x = -2.769008418Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.105991582, -2.769008418}
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