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Simplifying 4x2 + -28x + -55 = 0 Reorder the terms: -55 + -28x + 4x2 = 0 Solving -55 + -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'. -13.75 + -7x + x2 = 0 Move the constant term to the right: Add '13.75' to each side of the equation. -13.75 + -7x + 13.75 + x2 = 0 + 13.75 Reorder the terms: -13.75 + 13.75 + -7x + x2 = 0 + 13.75 Combine like terms: -13.75 + 13.75 = 0.00 0.00 + -7x + x2 = 0 + 13.75 -7x + x2 = 0 + 13.75 Combine like terms: 0 + 13.75 = 13.75 -7x + x2 = 13.75 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 = 13.75 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 13.75 + 12.25 Combine like terms: 13.75 + 12.25 = 26 12.25 + -7x + x2 = 26 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 26 Calculate the square root of the right side: 5.099019514 Break this problem into two subproblems by setting (x + -3.5) equal to 5.099019514 and -5.099019514.Subproblem 1
x + -3.5 = 5.099019514 Simplifying x + -3.5 = 5.099019514 Reorder the terms: -3.5 + x = 5.099019514 Solving -3.5 + x = 5.099019514 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 = 5.099019514 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 5.099019514 + 3.5 x = 5.099019514 + 3.5 Combine like terms: 5.099019514 + 3.5 = 8.599019514 x = 8.599019514 Simplifying x = 8.599019514Subproblem 2
x + -3.5 = -5.099019514 Simplifying x + -3.5 = -5.099019514 Reorder the terms: -3.5 + x = -5.099019514 Solving -3.5 + x = -5.099019514 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 = -5.099019514 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -5.099019514 + 3.5 x = -5.099019514 + 3.5 Combine like terms: -5.099019514 + 3.5 = -1.599019514 x = -1.599019514 Simplifying x = -1.599019514Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.599019514, -1.599019514}
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