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Simplifying 4x2 + 27x + 16 = 0 Reorder the terms: 16 + 27x + 4x2 = 0 Solving 16 + 27x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 4 + 6.75x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + 6.75x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + 6.75x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 6.75x + x2 = 0 + -4 6.75x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 6.75x + x2 = -4 The x term is 6.75x. Take half its coefficient (3.375). Square it (11.390625) and add it to both sides. Add '11.390625' to each side of the equation. 6.75x + 11.390625 + x2 = -4 + 11.390625 Reorder the terms: 11.390625 + 6.75x + x2 = -4 + 11.390625 Combine like terms: -4 + 11.390625 = 7.390625 11.390625 + 6.75x + x2 = 7.390625 Factor a perfect square on the left side: (x + 3.375)(x + 3.375) = 7.390625 Calculate the square root of the right side: 2.718570396 Break this problem into two subproblems by setting (x + 3.375) equal to 2.718570396 and -2.718570396.Subproblem 1
x + 3.375 = 2.718570396 Simplifying x + 3.375 = 2.718570396 Reorder the terms: 3.375 + x = 2.718570396 Solving 3.375 + x = 2.718570396 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.375' to each side of the equation. 3.375 + -3.375 + x = 2.718570396 + -3.375 Combine like terms: 3.375 + -3.375 = 0.000 0.000 + x = 2.718570396 + -3.375 x = 2.718570396 + -3.375 Combine like terms: 2.718570396 + -3.375 = -0.656429604 x = -0.656429604 Simplifying x = -0.656429604Subproblem 2
x + 3.375 = -2.718570396 Simplifying x + 3.375 = -2.718570396 Reorder the terms: 3.375 + x = -2.718570396 Solving 3.375 + x = -2.718570396 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.375' to each side of the equation. 3.375 + -3.375 + x = -2.718570396 + -3.375 Combine like terms: 3.375 + -3.375 = 0.000 0.000 + x = -2.718570396 + -3.375 x = -2.718570396 + -3.375 Combine like terms: -2.718570396 + -3.375 = -6.093570396 x = -6.093570396 Simplifying x = -6.093570396Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.656429604, -6.093570396}
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