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Simplifying 3x = -16x2 + -4x + 1 Reorder the terms: 3x = 1 + -4x + -16x2 Solving 3x = 1 + -4x + -16x2 Solving for variable 'x'. Reorder the terms: -1 + 3x + 4x + 16x2 = 1 + -4x + -16x2 + -1 + 4x + 16x2 Combine like terms: 3x + 4x = 7x -1 + 7x + 16x2 = 1 + -4x + -16x2 + -1 + 4x + 16x2 Reorder the terms: -1 + 7x + 16x2 = 1 + -1 + -4x + 4x + -16x2 + 16x2 Combine like terms: 1 + -1 = 0 -1 + 7x + 16x2 = 0 + -4x + 4x + -16x2 + 16x2 -1 + 7x + 16x2 = -4x + 4x + -16x2 + 16x2 Combine like terms: -4x + 4x = 0 -1 + 7x + 16x2 = 0 + -16x2 + 16x2 -1 + 7x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -1 + 7x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.0625 + 0.4375x + x2 = 0 Move the constant term to the right: Add '0.0625' to each side of the equation. -0.0625 + 0.4375x + 0.0625 + x2 = 0 + 0.0625 Reorder the terms: -0.0625 + 0.0625 + 0.4375x + x2 = 0 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + 0.4375x + x2 = 0 + 0.0625 0.4375x + x2 = 0 + 0.0625 Combine like terms: 0 + 0.0625 = 0.0625 0.4375x + x2 = 0.0625 The x term is 0.4375x. Take half its coefficient (0.21875). Square it (0.0478515625) and add it to both sides. Add '0.0478515625' to each side of the equation. 0.4375x + 0.0478515625 + x2 = 0.0625 + 0.0478515625 Reorder the terms: 0.0478515625 + 0.4375x + x2 = 0.0625 + 0.0478515625 Combine like terms: 0.0625 + 0.0478515625 = 0.1103515625 0.0478515625 + 0.4375x + x2 = 0.1103515625 Factor a perfect square on the left side: (x + 0.21875)(x + 0.21875) = 0.1103515625 Calculate the square root of the right side: 0.332192057 Break this problem into two subproblems by setting (x + 0.21875) equal to 0.332192057 and -0.332192057.Subproblem 1
x + 0.21875 = 0.332192057 Simplifying x + 0.21875 = 0.332192057 Reorder the terms: 0.21875 + x = 0.332192057 Solving 0.21875 + x = 0.332192057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.21875' to each side of the equation. 0.21875 + -0.21875 + x = 0.332192057 + -0.21875 Combine like terms: 0.21875 + -0.21875 = 0.00000 0.00000 + x = 0.332192057 + -0.21875 x = 0.332192057 + -0.21875 Combine like terms: 0.332192057 + -0.21875 = 0.113442057 x = 0.113442057 Simplifying x = 0.113442057Subproblem 2
x + 0.21875 = -0.332192057 Simplifying x + 0.21875 = -0.332192057 Reorder the terms: 0.21875 + x = -0.332192057 Solving 0.21875 + x = -0.332192057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.21875' to each side of the equation. 0.21875 + -0.21875 + x = -0.332192057 + -0.21875 Combine like terms: 0.21875 + -0.21875 = 0.00000 0.00000 + x = -0.332192057 + -0.21875 x = -0.332192057 + -0.21875 Combine like terms: -0.332192057 + -0.21875 = -0.550942057 x = -0.550942057 Simplifying x = -0.550942057Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.113442057, -0.550942057}
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