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Simplifying 4x2 + -28x + 41 = 0 Reorder the terms: 41 + -28x + 4x2 = 0 Solving 41 + -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'. 10.25 + -7x + x2 = 0 Move the constant term to the right: Add '-10.25' to each side of the equation. 10.25 + -7x + -10.25 + x2 = 0 + -10.25 Reorder the terms: 10.25 + -10.25 + -7x + x2 = 0 + -10.25 Combine like terms: 10.25 + -10.25 = 0.00 0.00 + -7x + x2 = 0 + -10.25 -7x + x2 = 0 + -10.25 Combine like terms: 0 + -10.25 = -10.25 -7x + x2 = -10.25 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 = -10.25 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -10.25 + 12.25 Combine like terms: -10.25 + 12.25 = 2 12.25 + -7x + x2 = 2 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (x + -3.5) equal to 1.414213562 and -1.414213562.Subproblem 1
x + -3.5 = 1.414213562 Simplifying x + -3.5 = 1.414213562 Reorder the terms: -3.5 + x = 1.414213562 Solving -3.5 + x = 1.414213562 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 = 1.414213562 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 1.414213562 + 3.5 x = 1.414213562 + 3.5 Combine like terms: 1.414213562 + 3.5 = 4.914213562 x = 4.914213562 Simplifying x = 4.914213562Subproblem 2
x + -3.5 = -1.414213562 Simplifying x + -3.5 = -1.414213562 Reorder the terms: -3.5 + x = -1.414213562 Solving -3.5 + x = -1.414213562 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 = -1.414213562 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -1.414213562 + 3.5 x = -1.414213562 + 3.5 Combine like terms: -1.414213562 + 3.5 = 2.085786438 x = 2.085786438 Simplifying x = 2.085786438Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.914213562, 2.085786438}
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