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Simplifying -2x2 + 87x + 90 = 0 Reorder the terms: 90 + 87x + -2x2 = 0 Solving 90 + 87x + -2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -45 + -43.5x + x2 = 0 Move the constant term to the right: Add '45' to each side of the equation. -45 + -43.5x + 45 + x2 = 0 + 45 Reorder the terms: -45 + 45 + -43.5x + x2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + -43.5x + x2 = 0 + 45 -43.5x + x2 = 0 + 45 Combine like terms: 0 + 45 = 45 -43.5x + x2 = 45 The x term is -43.5x. Take half its coefficient (-21.75). Square it (473.0625) and add it to both sides. Add '473.0625' to each side of the equation. -43.5x + 473.0625 + x2 = 45 + 473.0625 Reorder the terms: 473.0625 + -43.5x + x2 = 45 + 473.0625 Combine like terms: 45 + 473.0625 = 518.0625 473.0625 + -43.5x + x2 = 518.0625 Factor a perfect square on the left side: (x + -21.75)(x + -21.75) = 518.0625 Calculate the square root of the right side: 22.760986358 Break this problem into two subproblems by setting (x + -21.75) equal to 22.760986358 and -22.760986358.Subproblem 1
x + -21.75 = 22.760986358 Simplifying x + -21.75 = 22.760986358 Reorder the terms: -21.75 + x = 22.760986358 Solving -21.75 + x = 22.760986358 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '21.75' to each side of the equation. -21.75 + 21.75 + x = 22.760986358 + 21.75 Combine like terms: -21.75 + 21.75 = 0.00 0.00 + x = 22.760986358 + 21.75 x = 22.760986358 + 21.75 Combine like terms: 22.760986358 + 21.75 = 44.510986358 x = 44.510986358 Simplifying x = 44.510986358Subproblem 2
x + -21.75 = -22.760986358 Simplifying x + -21.75 = -22.760986358 Reorder the terms: -21.75 + x = -22.760986358 Solving -21.75 + x = -22.760986358 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '21.75' to each side of the equation. -21.75 + 21.75 + x = -22.760986358 + 21.75 Combine like terms: -21.75 + 21.75 = 0.00 0.00 + x = -22.760986358 + 21.75 x = -22.760986358 + 21.75 Combine like terms: -22.760986358 + 21.75 = -1.010986358 x = -1.010986358 Simplifying x = -1.010986358Solution
The solution to the problem is based on the solutions from the subproblems. x = {44.510986358, -1.010986358}
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