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Simplifying 16x2 + 34x + -7 = 0 Reorder the terms: -7 + 34x + 16x2 = 0 Solving -7 + 34x + 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'. -0.4375 + 2.125x + x2 = 0 Move the constant term to the right: Add '0.4375' to each side of the equation. -0.4375 + 2.125x + 0.4375 + x2 = 0 + 0.4375 Reorder the terms: -0.4375 + 0.4375 + 2.125x + x2 = 0 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + 2.125x + x2 = 0 + 0.4375 2.125x + x2 = 0 + 0.4375 Combine like terms: 0 + 0.4375 = 0.4375 2.125x + x2 = 0.4375 The x term is 2.125x. Take half its coefficient (1.0625). Square it (1.12890625) and add it to both sides. Add '1.12890625' to each side of the equation. 2.125x + 1.12890625 + x2 = 0.4375 + 1.12890625 Reorder the terms: 1.12890625 + 2.125x + x2 = 0.4375 + 1.12890625 Combine like terms: 0.4375 + 1.12890625 = 1.56640625 1.12890625 + 2.125x + x2 = 1.56640625 Factor a perfect square on the left side: (x + 1.0625)(x + 1.0625) = 1.56640625 Calculate the square root of the right side: 1.251561525 Break this problem into two subproblems by setting (x + 1.0625) equal to 1.251561525 and -1.251561525.Subproblem 1
x + 1.0625 = 1.251561525 Simplifying x + 1.0625 = 1.251561525 Reorder the terms: 1.0625 + x = 1.251561525 Solving 1.0625 + x = 1.251561525 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.0625' to each side of the equation. 1.0625 + -1.0625 + x = 1.251561525 + -1.0625 Combine like terms: 1.0625 + -1.0625 = 0.0000 0.0000 + x = 1.251561525 + -1.0625 x = 1.251561525 + -1.0625 Combine like terms: 1.251561525 + -1.0625 = 0.189061525 x = 0.189061525 Simplifying x = 0.189061525Subproblem 2
x + 1.0625 = -1.251561525 Simplifying x + 1.0625 = -1.251561525 Reorder the terms: 1.0625 + x = -1.251561525 Solving 1.0625 + x = -1.251561525 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.0625' to each side of the equation. 1.0625 + -1.0625 + x = -1.251561525 + -1.0625 Combine like terms: 1.0625 + -1.0625 = 0.0000 0.0000 + x = -1.251561525 + -1.0625 x = -1.251561525 + -1.0625 Combine like terms: -1.251561525 + -1.0625 = -2.314061525 x = -2.314061525 Simplifying x = -2.314061525Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.189061525, -2.314061525}
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