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Simplifying 4x2 + -28x + 11 = 0 Reorder the terms: 11 + -28x + 4x2 = 0 Solving 11 + -28x + 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 + -7x + x2 = 0 Move the constant term to the right: Add '-2.75' to each side of the equation. 2.75 + -7x + -2.75 + x2 = 0 + -2.75 Reorder the terms: 2.75 + -2.75 + -7x + x2 = 0 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + -7x + x2 = 0 + -2.75 -7x + x2 = 0 + -2.75 Combine like terms: 0 + -2.75 = -2.75 -7x + x2 = -2.75 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = -2.75 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -2.75 + 12.25 Combine like terms: -2.75 + 12.25 = 9.5 12.25 + -7x + x2 = 9.5 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 9.5 Calculate the square root of the right side: 3.082207001 Break this problem into two subproblems by setting (x + -3.5) equal to 3.082207001 and -3.082207001.Subproblem 1
x + -3.5 = 3.082207001 Simplifying x + -3.5 = 3.082207001 Reorder the terms: -3.5 + x = 3.082207001 Solving -3.5 + x = 3.082207001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 3.082207001 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 3.082207001 + 3.5 x = 3.082207001 + 3.5 Combine like terms: 3.082207001 + 3.5 = 6.582207001 x = 6.582207001 Simplifying x = 6.582207001Subproblem 2
x + -3.5 = -3.082207001 Simplifying x + -3.5 = -3.082207001 Reorder the terms: -3.5 + x = -3.082207001 Solving -3.5 + x = -3.082207001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -3.082207001 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -3.082207001 + 3.5 x = -3.082207001 + 3.5 Combine like terms: -3.082207001 + 3.5 = 0.417792999 x = 0.417792999 Simplifying x = 0.417792999Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.582207001, 0.417792999}
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