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Simplifying 16x2 + -112x + 25 = 0 Reorder the terms: 25 + -112x + 16x2 = 0 Solving 25 + -112x + 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'. 1.5625 + -7x + x2 = 0 Move the constant term to the right: Add '-1.5625' to each side of the equation. 1.5625 + -7x + -1.5625 + x2 = 0 + -1.5625 Reorder the terms: 1.5625 + -1.5625 + -7x + x2 = 0 + -1.5625 Combine like terms: 1.5625 + -1.5625 = 0.0000 0.0000 + -7x + x2 = 0 + -1.5625 -7x + x2 = 0 + -1.5625 Combine like terms: 0 + -1.5625 = -1.5625 -7x + x2 = -1.5625 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = -1.5625 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -1.5625 + 12.25 Combine like terms: -1.5625 + 12.25 = 10.6875 12.25 + -7x + x2 = 10.6875 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 10.6875 Calculate the square root of the right side: 3.269174208 Break this problem into two subproblems by setting (x + -3.5) equal to 3.269174208 and -3.269174208.Subproblem 1
x + -3.5 = 3.269174208 Simplifying x + -3.5 = 3.269174208 Reorder the terms: -3.5 + x = 3.269174208 Solving -3.5 + x = 3.269174208 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 3.269174208 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 3.269174208 + 3.5 x = 3.269174208 + 3.5 Combine like terms: 3.269174208 + 3.5 = 6.769174208 x = 6.769174208 Simplifying x = 6.769174208Subproblem 2
x + -3.5 = -3.269174208 Simplifying x + -3.5 = -3.269174208 Reorder the terms: -3.5 + x = -3.269174208 Solving -3.5 + x = -3.269174208 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -3.269174208 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -3.269174208 + 3.5 x = -3.269174208 + 3.5 Combine like terms: -3.269174208 + 3.5 = 0.230825792 x = 0.230825792 Simplifying x = 0.230825792Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.769174208, 0.230825792}
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