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Simplifying -4x2 + 13x + 20 = 0 Reorder the terms: 20 + 13x + -4x2 = 0 Solving 20 + 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'. -5 + -3.25x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -3.25x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -3.25x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -3.25x + x2 = 0 + 5 -3.25x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -3.25x + x2 = 5 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 = 5 + 2.640625 Reorder the terms: 2.640625 + -3.25x + x2 = 5 + 2.640625 Combine like terms: 5 + 2.640625 = 7.640625 2.640625 + -3.25x + x2 = 7.640625 Factor a perfect square on the left side: (x + -1.625)(x + -1.625) = 7.640625 Calculate the square root of the right side: 2.764168048 Break this problem into two subproblems by setting (x + -1.625) equal to 2.764168048 and -2.764168048.Subproblem 1
x + -1.625 = 2.764168048 Simplifying x + -1.625 = 2.764168048 Reorder the terms: -1.625 + x = 2.764168048 Solving -1.625 + x = 2.764168048 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 = 2.764168048 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + x = 2.764168048 + 1.625 x = 2.764168048 + 1.625 Combine like terms: 2.764168048 + 1.625 = 4.389168048 x = 4.389168048 Simplifying x = 4.389168048Subproblem 2
x + -1.625 = -2.764168048 Simplifying x + -1.625 = -2.764168048 Reorder the terms: -1.625 + x = -2.764168048 Solving -1.625 + x = -2.764168048 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 = -2.764168048 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + x = -2.764168048 + 1.625 x = -2.764168048 + 1.625 Combine like terms: -2.764168048 + 1.625 = -1.139168048 x = -1.139168048 Simplifying x = -1.139168048Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.389168048, -1.139168048}
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