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Simplifying 4x2 + -13x + -28 = 0 Reorder the terms: -28 + -13x + 4x2 = 0 Solving -28 + -13x + 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'. -7 + -3.25x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + -3.25x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + -3.25x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -3.25x + x2 = 0 + 7 -3.25x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 -3.25x + x2 = 7 The x term is -3.25x. Take half its coefficient (-1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. -3.25x + 2.640625 + x2 = 7 + 2.640625 Reorder the terms: 2.640625 + -3.25x + x2 = 7 + 2.640625 Combine like terms: 7 + 2.640625 = 9.640625 2.640625 + -3.25x + x2 = 9.640625 Factor a perfect square on the left side: (x + -1.625)(x + -1.625) = 9.640625 Calculate the square root of the right side: 3.104935587 Break this problem into two subproblems by setting (x + -1.625) equal to 3.104935587 and -3.104935587.Subproblem 1
x + -1.625 = 3.104935587 Simplifying x + -1.625 = 3.104935587 Reorder the terms: -1.625 + x = 3.104935587 Solving -1.625 + x = 3.104935587 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + x = 3.104935587 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + x = 3.104935587 + 1.625 x = 3.104935587 + 1.625 Combine like terms: 3.104935587 + 1.625 = 4.729935587 x = 4.729935587 Simplifying x = 4.729935587Subproblem 2
x + -1.625 = -3.104935587 Simplifying x + -1.625 = -3.104935587 Reorder the terms: -1.625 + x = -3.104935587 Solving -1.625 + x = -3.104935587 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + x = -3.104935587 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + x = -3.104935587 + 1.625 x = -3.104935587 + 1.625 Combine like terms: -3.104935587 + 1.625 = -1.479935587 x = -1.479935587 Simplifying x = -1.479935587Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.729935587, -1.479935587}
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