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Simplifying x + (x + 89)(x + -20) = 180 Reorder the terms: x + (89 + x)(x + -20) = 180 Reorder the terms: x + (89 + x)(-20 + x) = 180 Multiply (89 + x) * (-20 + x) x + (89(-20 + x) + x(-20 + x)) = 180 x + ((-20 * 89 + x * 89) + x(-20 + x)) = 180 x + ((-1780 + 89x) + x(-20 + x)) = 180 x + (-1780 + 89x + (-20 * x + x * x)) = 180 x + (-1780 + 89x + (-20x + x2)) = 180 Combine like terms: 89x + -20x = 69x x + (-1780 + 69x + x2) = 180 Reorder the terms: -1780 + x + 69x + x2 = 180 Combine like terms: x + 69x = 70x -1780 + 70x + x2 = 180 Solving -1780 + 70x + x2 = 180 Solving for variable 'x'. Reorder the terms: -1780 + -180 + 70x + x2 = 180 + -180 Combine like terms: -1780 + -180 = -1960 -1960 + 70x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -1960 + 70x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1960' to each side of the equation. -1960 + 70x + 1960 + x2 = 0 + 1960 Reorder the terms: -1960 + 1960 + 70x + x2 = 0 + 1960 Combine like terms: -1960 + 1960 = 0 0 + 70x + x2 = 0 + 1960 70x + x2 = 0 + 1960 Combine like terms: 0 + 1960 = 1960 70x + x2 = 1960 The x term is 70x. Take half its coefficient (35). Square it (1225) and add it to both sides. Add '1225' to each side of the equation. 70x + 1225 + x2 = 1960 + 1225 Reorder the terms: 1225 + 70x + x2 = 1960 + 1225 Combine like terms: 1960 + 1225 = 3185 1225 + 70x + x2 = 3185 Factor a perfect square on the left side: (x + 35)(x + 35) = 3185 Calculate the square root of the right side: 56.435804238 Break this problem into two subproblems by setting (x + 35) equal to 56.435804238 and -56.435804238.Subproblem 1
x + 35 = 56.435804238 Simplifying x + 35 = 56.435804238 Reorder the terms: 35 + x = 56.435804238 Solving 35 + x = 56.435804238 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-35' to each side of the equation. 35 + -35 + x = 56.435804238 + -35 Combine like terms: 35 + -35 = 0 0 + x = 56.435804238 + -35 x = 56.435804238 + -35 Combine like terms: 56.435804238 + -35 = 21.435804238 x = 21.435804238 Simplifying x = 21.435804238Subproblem 2
x + 35 = -56.435804238 Simplifying x + 35 = -56.435804238 Reorder the terms: 35 + x = -56.435804238 Solving 35 + x = -56.435804238 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-35' to each side of the equation. 35 + -35 + x = -56.435804238 + -35 Combine like terms: 35 + -35 = 0 0 + x = -56.435804238 + -35 x = -56.435804238 + -35 Combine like terms: -56.435804238 + -35 = -91.435804238 x = -91.435804238 Simplifying x = -91.435804238Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.435804238, -91.435804238}
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