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Simplifying 16x2 + -58x + 10 = 0 Reorder the terms: 10 + -58x + 16x2 = 0 Solving 10 + -58x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + -29x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -29x + 8x2)' equal to zero and attempt to solve: Simplifying 5 + -29x + 8x2 = 0 Solving 5 + -29x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.625 + -3.625x + x2 = 0 Move the constant term to the right: Add '-0.625' to each side of the equation. 0.625 + -3.625x + -0.625 + x2 = 0 + -0.625 Reorder the terms: 0.625 + -0.625 + -3.625x + x2 = 0 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + -3.625x + x2 = 0 + -0.625 -3.625x + x2 = 0 + -0.625 Combine like terms: 0 + -0.625 = -0.625 -3.625x + x2 = -0.625 The x term is -3.625x. Take half its coefficient (-1.8125). Square it (3.28515625) and add it to both sides. Add '3.28515625' to each side of the equation. -3.625x + 3.28515625 + x2 = -0.625 + 3.28515625 Reorder the terms: 3.28515625 + -3.625x + x2 = -0.625 + 3.28515625 Combine like terms: -0.625 + 3.28515625 = 2.66015625 3.28515625 + -3.625x + x2 = 2.66015625 Factor a perfect square on the left side: (x + -1.8125)(x + -1.8125) = 2.66015625 Calculate the square root of the right side: 1.630998544 Break this problem into two subproblems by setting (x + -1.8125) equal to 1.630998544 and -1.630998544.Subproblem 1
x + -1.8125 = 1.630998544 Simplifying x + -1.8125 = 1.630998544 Reorder the terms: -1.8125 + x = 1.630998544 Solving -1.8125 + x = 1.630998544 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8125' to each side of the equation. -1.8125 + 1.8125 + x = 1.630998544 + 1.8125 Combine like terms: -1.8125 + 1.8125 = 0.0000 0.0000 + x = 1.630998544 + 1.8125 x = 1.630998544 + 1.8125 Combine like terms: 1.630998544 + 1.8125 = 3.443498544 x = 3.443498544 Simplifying x = 3.443498544Subproblem 2
x + -1.8125 = -1.630998544 Simplifying x + -1.8125 = -1.630998544 Reorder the terms: -1.8125 + x = -1.630998544 Solving -1.8125 + x = -1.630998544 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8125' to each side of the equation. -1.8125 + 1.8125 + x = -1.630998544 + 1.8125 Combine like terms: -1.8125 + 1.8125 = 0.0000 0.0000 + x = -1.630998544 + 1.8125 x = -1.630998544 + 1.8125 Combine like terms: -1.630998544 + 1.8125 = 0.181501456 x = 0.181501456 Simplifying x = 0.181501456Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.443498544, 0.181501456}Solution
x = {3.443498544, 0.181501456}
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