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Simplifying (4x2) + -11x + -90 = 0 Reorder the terms: -90 + -11x + (4x2) = 0 Solving -90 + -11x + (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'. -22.5 + -2.75x + x2 = 0 Move the constant term to the right: Add '22.5' to each side of the equation. -22.5 + -2.75x + 22.5 + x2 = 0 + 22.5 Reorder the terms: -22.5 + 22.5 + -2.75x + x2 = 0 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + -2.75x + x2 = 0 + 22.5 -2.75x + x2 = 0 + 22.5 Combine like terms: 0 + 22.5 = 22.5 -2.75x + x2 = 22.5 The x term is -2.75x. Take half its coefficient (-1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. -2.75x + 1.890625 + x2 = 22.5 + 1.890625 Reorder the terms: 1.890625 + -2.75x + x2 = 22.5 + 1.890625 Combine like terms: 22.5 + 1.890625 = 24.390625 1.890625 + -2.75x + x2 = 24.390625 Factor a perfect square on the left side: ((x) + -1.375)((x) + -1.375) = 24.390625 Calculate the square root of the right side: 4.938686566 Break this problem into two subproblems by setting ((x) + -1.375) equal to 4.938686566 and -4.938686566.Subproblem 1
(x) + -1.375 = 4.938686566 Simplifying (x) + -1.375 = 4.938686566 x + -1.375 = 4.938686566 Reorder the terms: -1.375 + x = 4.938686566 Solving -1.375 + x = 4.938686566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = 4.938686566 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = 4.938686566 + 1.375 x = 4.938686566 + 1.375 Combine like terms: 4.938686566 + 1.375 = 6.313686566 x = 6.313686566 Simplifying x = 6.313686566Subproblem 2
(x) + -1.375 = -4.938686566 Simplifying (x) + -1.375 = -4.938686566 x + -1.375 = -4.938686566 Reorder the terms: -1.375 + x = -4.938686566 Solving -1.375 + x = -4.938686566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = -4.938686566 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = -4.938686566 + 1.375 x = -4.938686566 + 1.375 Combine like terms: -4.938686566 + 1.375 = -3.563686566 x = -3.563686566 Simplifying x = -3.563686566Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.313686566, -3.563686566}
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