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Simplifying 80x + 800 = x2 + 20x Reorder the terms: 800 + 80x = x2 + 20x Reorder the terms: 800 + 80x = 20x + x2 Solving 800 + 80x = 20x + x2 Solving for variable 'x'. Combine like terms: 80x + -20x = 60x 800 + 60x + -1x2 = 20x + x2 + -20x + -1x2 Reorder the terms: 800 + 60x + -1x2 = 20x + -20x + x2 + -1x2 Combine like terms: 20x + -20x = 0 800 + 60x + -1x2 = 0 + x2 + -1x2 800 + 60x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 800 + 60x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -800 + -60x + x2 = 0 Move the constant term to the right: Add '800' to each side of the equation. -800 + -60x + 800 + x2 = 0 + 800 Reorder the terms: -800 + 800 + -60x + x2 = 0 + 800 Combine like terms: -800 + 800 = 0 0 + -60x + x2 = 0 + 800 -60x + x2 = 0 + 800 Combine like terms: 0 + 800 = 800 -60x + x2 = 800 The x term is -60x. Take half its coefficient (-30). Square it (900) and add it to both sides. Add '900' to each side of the equation. -60x + 900 + x2 = 800 + 900 Reorder the terms: 900 + -60x + x2 = 800 + 900 Combine like terms: 800 + 900 = 1700 900 + -60x + x2 = 1700 Factor a perfect square on the left side: (x + -30)(x + -30) = 1700 Calculate the square root of the right side: 41.231056256 Break this problem into two subproblems by setting (x + -30) equal to 41.231056256 and -41.231056256.Subproblem 1
x + -30 = 41.231056256 Simplifying x + -30 = 41.231056256 Reorder the terms: -30 + x = 41.231056256 Solving -30 + x = 41.231056256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = 41.231056256 + 30 Combine like terms: -30 + 30 = 0 0 + x = 41.231056256 + 30 x = 41.231056256 + 30 Combine like terms: 41.231056256 + 30 = 71.231056256 x = 71.231056256 Simplifying x = 71.231056256Subproblem 2
x + -30 = -41.231056256 Simplifying x + -30 = -41.231056256 Reorder the terms: -30 + x = -41.231056256 Solving -30 + x = -41.231056256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = -41.231056256 + 30 Combine like terms: -30 + 30 = 0 0 + x = -41.231056256 + 30 x = -41.231056256 + 30 Combine like terms: -41.231056256 + 30 = -11.231056256 x = -11.231056256 Simplifying x = -11.231056256Solution
The solution to the problem is based on the solutions from the subproblems. x = {71.231056256, -11.231056256}
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