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Simplifying 16x2 + 2x + -4 = 445 Reorder the terms: -4 + 2x + 16x2 = 445 Solving -4 + 2x + 16x2 = 445 Solving for variable 'x'. Reorder the terms: -4 + -445 + 2x + 16x2 = 445 + -445 Combine like terms: -4 + -445 = -449 -449 + 2x + 16x2 = 445 + -445 Combine like terms: 445 + -445 = 0 -449 + 2x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -28.0625 + 0.125x + x2 = 0 Move the constant term to the right: Add '28.0625' to each side of the equation. -28.0625 + 0.125x + 28.0625 + x2 = 0 + 28.0625 Reorder the terms: -28.0625 + 28.0625 + 0.125x + x2 = 0 + 28.0625 Combine like terms: -28.0625 + 28.0625 = 0.0000 0.0000 + 0.125x + x2 = 0 + 28.0625 0.125x + x2 = 0 + 28.0625 Combine like terms: 0 + 28.0625 = 28.0625 0.125x + x2 = 28.0625 The x term is 0.125x. Take half its coefficient (0.0625). Square it (0.00390625) and add it to both sides. Add '0.00390625' to each side of the equation. 0.125x + 0.00390625 + x2 = 28.0625 + 0.00390625 Reorder the terms: 0.00390625 + 0.125x + x2 = 28.0625 + 0.00390625 Combine like terms: 28.0625 + 0.00390625 = 28.06640625 0.00390625 + 0.125x + x2 = 28.06640625 Factor a perfect square on the left side: (x + 0.0625)(x + 0.0625) = 28.06640625 Calculate the square root of the right side: 5.297773707 Break this problem into two subproblems by setting (x + 0.0625) equal to 5.297773707 and -5.297773707.Subproblem 1
x + 0.0625 = 5.297773707 Simplifying x + 0.0625 = 5.297773707 Reorder the terms: 0.0625 + x = 5.297773707 Solving 0.0625 + x = 5.297773707 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0625' to each side of the equation. 0.0625 + -0.0625 + x = 5.297773707 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + x = 5.297773707 + -0.0625 x = 5.297773707 + -0.0625 Combine like terms: 5.297773707 + -0.0625 = 5.235273707 x = 5.235273707 Simplifying x = 5.235273707Subproblem 2
x + 0.0625 = -5.297773707 Simplifying x + 0.0625 = -5.297773707 Reorder the terms: 0.0625 + x = -5.297773707 Solving 0.0625 + x = -5.297773707 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0625' to each side of the equation. 0.0625 + -0.0625 + x = -5.297773707 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + x = -5.297773707 + -0.0625 x = -5.297773707 + -0.0625 Combine like terms: -5.297773707 + -0.0625 = -5.360273707 x = -5.360273707 Simplifying x = -5.360273707Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.235273707, -5.360273707}
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