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Simplifying 16x2 + -56x + 49 = 28 Reorder the terms: 49 + -56x + 16x2 = 28 Solving 49 + -56x + 16x2 = 28 Solving for variable 'x'. Reorder the terms: 49 + -28 + -56x + 16x2 = 28 + -28 Combine like terms: 49 + -28 = 21 21 + -56x + 16x2 = 28 + -28 Combine like terms: 28 + -28 = 0 21 + -56x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 1.3125 + -3.5x + x2 = 0 Move the constant term to the right: Add '-1.3125' to each side of the equation. 1.3125 + -3.5x + -1.3125 + x2 = 0 + -1.3125 Reorder the terms: 1.3125 + -1.3125 + -3.5x + x2 = 0 + -1.3125 Combine like terms: 1.3125 + -1.3125 = 0.0000 0.0000 + -3.5x + x2 = 0 + -1.3125 -3.5x + x2 = 0 + -1.3125 Combine like terms: 0 + -1.3125 = -1.3125 -3.5x + x2 = -1.3125 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = -1.3125 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = -1.3125 + 3.0625 Combine like terms: -1.3125 + 3.0625 = 1.75 3.0625 + -3.5x + x2 = 1.75 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 1.75 Calculate the square root of the right side: 1.322875656 Break this problem into two subproblems by setting (x + -1.75) equal to 1.322875656 and -1.322875656.Subproblem 1
x + -1.75 = 1.322875656 Simplifying x + -1.75 = 1.322875656 Reorder the terms: -1.75 + x = 1.322875656 Solving -1.75 + x = 1.322875656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 1.322875656 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 1.322875656 + 1.75 x = 1.322875656 + 1.75 Combine like terms: 1.322875656 + 1.75 = 3.072875656 x = 3.072875656 Simplifying x = 3.072875656Subproblem 2
x + -1.75 = -1.322875656 Simplifying x + -1.75 = -1.322875656 Reorder the terms: -1.75 + x = -1.322875656 Solving -1.75 + x = -1.322875656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -1.322875656 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -1.322875656 + 1.75 x = -1.322875656 + 1.75 Combine like terms: -1.322875656 + 1.75 = 0.427124344 x = 0.427124344 Simplifying x = 0.427124344Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.072875656, 0.427124344}
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