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Simplifying 16x2 + -16x + 4 = 11 Reorder the terms: 4 + -16x + 16x2 = 11 Solving 4 + -16x + 16x2 = 11 Solving for variable 'x'. Reorder the terms: 4 + -11 + -16x + 16x2 = 11 + -11 Combine like terms: 4 + -11 = -7 -7 + -16x + 16x2 = 11 + -11 Combine like terms: 11 + -11 = 0 -7 + -16x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.4375 + -1x + x2 = 0 Move the constant term to the right: Add '0.4375' to each side of the equation. -0.4375 + -1x + 0.4375 + x2 = 0 + 0.4375 Reorder the terms: -0.4375 + 0.4375 + -1x + x2 = 0 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + -1x + x2 = 0 + 0.4375 -1x + x2 = 0 + 0.4375 Combine like terms: 0 + 0.4375 = 0.4375 -1x + x2 = 0.4375 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 0.4375 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 0.4375 + 0.25 Combine like terms: 0.4375 + 0.25 = 0.6875 0.25 + -1x + x2 = 0.6875 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.6875 Calculate the square root of the right side: 0.829156198 Break this problem into two subproblems by setting (x + -0.5) equal to 0.829156198 and -0.829156198.Subproblem 1
x + -0.5 = 0.829156198 Simplifying x + -0.5 = 0.829156198 Reorder the terms: -0.5 + x = 0.829156198 Solving -0.5 + x = 0.829156198 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0.829156198 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.829156198 + 0.5 x = 0.829156198 + 0.5 Combine like terms: 0.829156198 + 0.5 = 1.329156198 x = 1.329156198 Simplifying x = 1.329156198Subproblem 2
x + -0.5 = -0.829156198 Simplifying x + -0.5 = -0.829156198 Reorder the terms: -0.5 + x = -0.829156198 Solving -0.5 + x = -0.829156198 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -0.829156198 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.829156198 + 0.5 x = -0.829156198 + 0.5 Combine like terms: -0.829156198 + 0.5 = -0.329156198 x = -0.329156198 Simplifying x = -0.329156198Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.329156198, -0.329156198}
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