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Simplifying 176x2 + -300x + 51 = 0 Reorder the terms: 51 + -300x + 176x2 = 0 Solving 51 + -300x + 176x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 176 the coefficient of the squared term: Divide each side by '176'. 0.2897727273 + -1.704545455x + x2 = 0 Move the constant term to the right: Add '-0.2897727273' to each side of the equation. 0.2897727273 + -1.704545455x + -0.2897727273 + x2 = 0 + -0.2897727273 Reorder the terms: 0.2897727273 + -0.2897727273 + -1.704545455x + x2 = 0 + -0.2897727273 Combine like terms: 0.2897727273 + -0.2897727273 = 0.0000000000 0.0000000000 + -1.704545455x + x2 = 0 + -0.2897727273 -1.704545455x + x2 = 0 + -0.2897727273 Combine like terms: 0 + -0.2897727273 = -0.2897727273 -1.704545455x + x2 = -0.2897727273 The x term is -1.704545455x. Take half its coefficient (-0.8522727275). Square it (0.7263688020) and add it to both sides. Add '0.7263688020' to each side of the equation. -1.704545455x + 0.7263688020 + x2 = -0.2897727273 + 0.7263688020 Reorder the terms: 0.7263688020 + -1.704545455x + x2 = -0.2897727273 + 0.7263688020 Combine like terms: -0.2897727273 + 0.7263688020 = 0.4365960747 0.7263688020 + -1.704545455x + x2 = 0.4365960747 Factor a perfect square on the left side: (x + -0.8522727275)(x + -0.8522727275) = 0.4365960747 Calculate the square root of the right side: 0.660754171 Break this problem into two subproblems by setting (x + -0.8522727275) equal to 0.660754171 and -0.660754171.Subproblem 1
x + -0.8522727275 = 0.660754171 Simplifying x + -0.8522727275 = 0.660754171 Reorder the terms: -0.8522727275 + x = 0.660754171 Solving -0.8522727275 + x = 0.660754171 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8522727275' to each side of the equation. -0.8522727275 + 0.8522727275 + x = 0.660754171 + 0.8522727275 Combine like terms: -0.8522727275 + 0.8522727275 = 0.0000000000 0.0000000000 + x = 0.660754171 + 0.8522727275 x = 0.660754171 + 0.8522727275 Combine like terms: 0.660754171 + 0.8522727275 = 1.5130268985 x = 1.5130268985 Simplifying x = 1.5130268985Subproblem 2
x + -0.8522727275 = -0.660754171 Simplifying x + -0.8522727275 = -0.660754171 Reorder the terms: -0.8522727275 + x = -0.660754171 Solving -0.8522727275 + x = -0.660754171 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8522727275' to each side of the equation. -0.8522727275 + 0.8522727275 + x = -0.660754171 + 0.8522727275 Combine like terms: -0.8522727275 + 0.8522727275 = 0.0000000000 0.0000000000 + x = -0.660754171 + 0.8522727275 x = -0.660754171 + 0.8522727275 Combine like terms: -0.660754171 + 0.8522727275 = 0.1915185565 x = 0.1915185565 Simplifying x = 0.1915185565Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5130268985, 0.1915185565}
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