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Simplifying 16x2 + -64x + 62 = 0 Reorder the terms: 62 + -64x + 16x2 = 0 Solving 62 + -64x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(31 + -32x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(31 + -32x + 8x2)' equal to zero and attempt to solve: Simplifying 31 + -32x + 8x2 = 0 Solving 31 + -32x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 3.875 + -4x + x2 = 0 Move the constant term to the right: Add '-3.875' to each side of the equation. 3.875 + -4x + -3.875 + x2 = 0 + -3.875 Reorder the terms: 3.875 + -3.875 + -4x + x2 = 0 + -3.875 Combine like terms: 3.875 + -3.875 = 0.000 0.000 + -4x + x2 = 0 + -3.875 -4x + x2 = 0 + -3.875 Combine like terms: 0 + -3.875 = -3.875 -4x + x2 = -3.875 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -3.875 + 4 Reorder the terms: 4 + -4x + x2 = -3.875 + 4 Combine like terms: -3.875 + 4 = 0.125 4 + -4x + x2 = 0.125 Factor a perfect square on the left side: (x + -2)(x + -2) = 0.125 Calculate the square root of the right side: 0.353553391 Break this problem into two subproblems by setting (x + -2) equal to 0.353553391 and -0.353553391.Subproblem 1
x + -2 = 0.353553391 Simplifying x + -2 = 0.353553391 Reorder the terms: -2 + x = 0.353553391 Solving -2 + x = 0.353553391 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 0.353553391 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0.353553391 + 2 x = 0.353553391 + 2 Combine like terms: 0.353553391 + 2 = 2.353553391 x = 2.353553391 Simplifying x = 2.353553391Subproblem 2
x + -2 = -0.353553391 Simplifying x + -2 = -0.353553391 Reorder the terms: -2 + x = -0.353553391 Solving -2 + x = -0.353553391 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -0.353553391 + 2 Combine like terms: -2 + 2 = 0 0 + x = -0.353553391 + 2 x = -0.353553391 + 2 Combine like terms: -0.353553391 + 2 = 1.646446609 x = 1.646446609 Simplifying x = 1.646446609Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.353553391, 1.646446609}Solution
x = {2.353553391, 1.646446609}
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