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Simplifying 4x2 + -28x + 5 = 0 Reorder the terms: 5 + -28x + 4x2 = 0 Solving 5 + -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'. 1.25 + -7x + x2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + -7x + -1.25 + x2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + -7x + x2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + -7x + x2 = 0 + -1.25 -7x + x2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 -7x + x2 = -1.25 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 = -1.25 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -1.25 + 12.25 Combine like terms: -1.25 + 12.25 = 11 12.25 + -7x + x2 = 11 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (x + -3.5) equal to 3.31662479 and -3.31662479.Subproblem 1
x + -3.5 = 3.31662479 Simplifying x + -3.5 = 3.31662479 Reorder the terms: -3.5 + x = 3.31662479 Solving -3.5 + x = 3.31662479 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 = 3.31662479 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 3.31662479 + 3.5 x = 3.31662479 + 3.5 Combine like terms: 3.31662479 + 3.5 = 6.81662479 x = 6.81662479 Simplifying x = 6.81662479Subproblem 2
x + -3.5 = -3.31662479 Simplifying x + -3.5 = -3.31662479 Reorder the terms: -3.5 + x = -3.31662479 Solving -3.5 + x = -3.31662479 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 = -3.31662479 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -3.31662479 + 3.5 x = -3.31662479 + 3.5 Combine like terms: -3.31662479 + 3.5 = 0.18337521 x = 0.18337521 Simplifying x = 0.18337521Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.81662479, 0.18337521}
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