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Simplifying 4x2 + -32x + 11 = 0 Reorder the terms: 11 + -32x + 4x2 = 0 Solving 11 + -32x + 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'. 2.75 + -8x + x2 = 0 Move the constant term to the right: Add '-2.75' to each side of the equation. 2.75 + -8x + -2.75 + x2 = 0 + -2.75 Reorder the terms: 2.75 + -2.75 + -8x + x2 = 0 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + -8x + x2 = 0 + -2.75 -8x + x2 = 0 + -2.75 Combine like terms: 0 + -2.75 = -2.75 -8x + x2 = -2.75 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -2.75 + 16 Reorder the terms: 16 + -8x + x2 = -2.75 + 16 Combine like terms: -2.75 + 16 = 13.25 16 + -8x + x2 = 13.25 Factor a perfect square on the left side: (x + -4)(x + -4) = 13.25 Calculate the square root of the right side: 3.640054945 Break this problem into two subproblems by setting (x + -4) equal to 3.640054945 and -3.640054945.Subproblem 1
x + -4 = 3.640054945 Simplifying x + -4 = 3.640054945 Reorder the terms: -4 + x = 3.640054945 Solving -4 + x = 3.640054945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 3.640054945 + 4 Combine like terms: -4 + 4 = 0 0 + x = 3.640054945 + 4 x = 3.640054945 + 4 Combine like terms: 3.640054945 + 4 = 7.640054945 x = 7.640054945 Simplifying x = 7.640054945Subproblem 2
x + -4 = -3.640054945 Simplifying x + -4 = -3.640054945 Reorder the terms: -4 + x = -3.640054945 Solving -4 + x = -3.640054945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -3.640054945 + 4 Combine like terms: -4 + 4 = 0 0 + x = -3.640054945 + 4 x = -3.640054945 + 4 Combine like terms: -3.640054945 + 4 = 0.359945055 x = 0.359945055 Simplifying x = 0.359945055Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.640054945, 0.359945055}
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