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Simplifying x(x + -20) = 84 Reorder the terms: x(-20 + x) = 84 (-20 * x + x * x) = 84 (-20x + x2) = 84 Solving -20x + x2 = 84 Solving for variable 'x'. Reorder the terms: -84 + -20x + x2 = 84 + -84 Combine like terms: 84 + -84 = 0 -84 + -20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '84' to each side of the equation. -84 + -20x + 84 + x2 = 0 + 84 Reorder the terms: -84 + 84 + -20x + x2 = 0 + 84 Combine like terms: -84 + 84 = 0 0 + -20x + x2 = 0 + 84 -20x + x2 = 0 + 84 Combine like terms: 0 + 84 = 84 -20x + x2 = 84 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = 84 + 100 Reorder the terms: 100 + -20x + x2 = 84 + 100 Combine like terms: 84 + 100 = 184 100 + -20x + x2 = 184 Factor a perfect square on the left side: (x + -10)(x + -10) = 184 Calculate the square root of the right side: 13.564659966 Break this problem into two subproblems by setting (x + -10) equal to 13.564659966 and -13.564659966.Subproblem 1
x + -10 = 13.564659966 Simplifying x + -10 = 13.564659966 Reorder the terms: -10 + x = 13.564659966 Solving -10 + x = 13.564659966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 13.564659966 + 10 Combine like terms: -10 + 10 = 0 0 + x = 13.564659966 + 10 x = 13.564659966 + 10 Combine like terms: 13.564659966 + 10 = 23.564659966 x = 23.564659966 Simplifying x = 23.564659966Subproblem 2
x + -10 = -13.564659966 Simplifying x + -10 = -13.564659966 Reorder the terms: -10 + x = -13.564659966 Solving -10 + x = -13.564659966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -13.564659966 + 10 Combine like terms: -10 + 10 = 0 0 + x = -13.564659966 + 10 x = -13.564659966 + 10 Combine like terms: -13.564659966 + 10 = -3.564659966 x = -3.564659966 Simplifying x = -3.564659966Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.564659966, -3.564659966}
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