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Simplifying 0 = 16x2 + -26x + 7 Reorder the terms: 0 = 7 + -26x + 16x2 Solving 0 = 7 + -26x + 16x2 Solving for variable 'x'. Combine like terms: 0 + -7 = -7 -7 + 26x + -16x2 = 7 + -26x + 16x2 + -7 + 26x + -16x2 Reorder the terms: -7 + 26x + -16x2 = 7 + -7 + -26x + 26x + 16x2 + -16x2 Combine like terms: 7 + -7 = 0 -7 + 26x + -16x2 = 0 + -26x + 26x + 16x2 + -16x2 -7 + 26x + -16x2 = -26x + 26x + 16x2 + -16x2 Combine like terms: -26x + 26x = 0 -7 + 26x + -16x2 = 0 + 16x2 + -16x2 -7 + 26x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 -7 + 26x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 0.4375 + -1.625x + x2 = 0 Move the constant term to the right: Add '-0.4375' to each side of the equation. 0.4375 + -1.625x + -0.4375 + x2 = 0 + -0.4375 Reorder the terms: 0.4375 + -0.4375 + -1.625x + x2 = 0 + -0.4375 Combine like terms: 0.4375 + -0.4375 = 0.0000 0.0000 + -1.625x + x2 = 0 + -0.4375 -1.625x + x2 = 0 + -0.4375 Combine like terms: 0 + -0.4375 = -0.4375 -1.625x + x2 = -0.4375 The x term is -1.625x. Take half its coefficient (-0.8125). Square it (0.66015625) and add it to both sides. Add '0.66015625' to each side of the equation. -1.625x + 0.66015625 + x2 = -0.4375 + 0.66015625 Reorder the terms: 0.66015625 + -1.625x + x2 = -0.4375 + 0.66015625 Combine like terms: -0.4375 + 0.66015625 = 0.22265625 0.66015625 + -1.625x + x2 = 0.22265625 Factor a perfect square on the left side: (x + -0.8125)(x + -0.8125) = 0.22265625 Calculate the square root of the right side: 0.471864652 Break this problem into two subproblems by setting (x + -0.8125) equal to 0.471864652 and -0.471864652.Subproblem 1
x + -0.8125 = 0.471864652 Simplifying x + -0.8125 = 0.471864652 Reorder the terms: -0.8125 + x = 0.471864652 Solving -0.8125 + x = 0.471864652 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8125' to each side of the equation. -0.8125 + 0.8125 + x = 0.471864652 + 0.8125 Combine like terms: -0.8125 + 0.8125 = 0.0000 0.0000 + x = 0.471864652 + 0.8125 x = 0.471864652 + 0.8125 Combine like terms: 0.471864652 + 0.8125 = 1.284364652 x = 1.284364652 Simplifying x = 1.284364652Subproblem 2
x + -0.8125 = -0.471864652 Simplifying x + -0.8125 = -0.471864652 Reorder the terms: -0.8125 + x = -0.471864652 Solving -0.8125 + x = -0.471864652 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8125' to each side of the equation. -0.8125 + 0.8125 + x = -0.471864652 + 0.8125 Combine like terms: -0.8125 + 0.8125 = 0.0000 0.0000 + x = -0.471864652 + 0.8125 x = -0.471864652 + 0.8125 Combine like terms: -0.471864652 + 0.8125 = 0.340635348 x = 0.340635348 Simplifying x = 0.340635348Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.284364652, 0.340635348}
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