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Simplifying x + (x + 89)(x + -20) = 360 Reorder the terms: x + (89 + x)(x + -20) = 360 Reorder the terms: x + (89 + x)(-20 + x) = 360 Multiply (89 + x) * (-20 + x) x + (89(-20 + x) + x(-20 + x)) = 360 x + ((-20 * 89 + x * 89) + x(-20 + x)) = 360 x + ((-1780 + 89x) + x(-20 + x)) = 360 x + (-1780 + 89x + (-20 * x + x * x)) = 360 x + (-1780 + 89x + (-20x + x2)) = 360 Combine like terms: 89x + -20x = 69x x + (-1780 + 69x + x2) = 360 Reorder the terms: -1780 + x + 69x + x2 = 360 Combine like terms: x + 69x = 70x -1780 + 70x + x2 = 360 Solving -1780 + 70x + x2 = 360 Solving for variable 'x'. Reorder the terms: -1780 + -360 + 70x + x2 = 360 + -360 Combine like terms: -1780 + -360 = -2140 -2140 + 70x + x2 = 360 + -360 Combine like terms: 360 + -360 = 0 -2140 + 70x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2140' to each side of the equation. -2140 + 70x + 2140 + x2 = 0 + 2140 Reorder the terms: -2140 + 2140 + 70x + x2 = 0 + 2140 Combine like terms: -2140 + 2140 = 0 0 + 70x + x2 = 0 + 2140 70x + x2 = 0 + 2140 Combine like terms: 0 + 2140 = 2140 70x + x2 = 2140 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 = 2140 + 1225 Reorder the terms: 1225 + 70x + x2 = 2140 + 1225 Combine like terms: 2140 + 1225 = 3365 1225 + 70x + x2 = 3365 Factor a perfect square on the left side: (x + 35)(x + 35) = 3365 Calculate the square root of the right side: 58.008620049 Break this problem into two subproblems by setting (x + 35) equal to 58.008620049 and -58.008620049.Subproblem 1
x + 35 = 58.008620049 Simplifying x + 35 = 58.008620049 Reorder the terms: 35 + x = 58.008620049 Solving 35 + x = 58.008620049 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 = 58.008620049 + -35 Combine like terms: 35 + -35 = 0 0 + x = 58.008620049 + -35 x = 58.008620049 + -35 Combine like terms: 58.008620049 + -35 = 23.008620049 x = 23.008620049 Simplifying x = 23.008620049Subproblem 2
x + 35 = -58.008620049 Simplifying x + 35 = -58.008620049 Reorder the terms: 35 + x = -58.008620049 Solving 35 + x = -58.008620049 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 = -58.008620049 + -35 Combine like terms: 35 + -35 = 0 0 + x = -58.008620049 + -35 x = -58.008620049 + -35 Combine like terms: -58.008620049 + -35 = -93.008620049 x = -93.008620049 Simplifying x = -93.008620049Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.008620049, -93.008620049}
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