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Simplifying x2 + 70x + -32100 = 0 Reorder the terms: -32100 + 70x + x2 = 0 Solving -32100 + 70x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '32100' to each side of the equation. -32100 + 70x + 32100 + x2 = 0 + 32100 Reorder the terms: -32100 + 32100 + 70x + x2 = 0 + 32100 Combine like terms: -32100 + 32100 = 0 0 + 70x + x2 = 0 + 32100 70x + x2 = 0 + 32100 Combine like terms: 0 + 32100 = 32100 70x + x2 = 32100 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 = 32100 + 1225 Reorder the terms: 1225 + 70x + x2 = 32100 + 1225 Combine like terms: 32100 + 1225 = 33325 1225 + 70x + x2 = 33325 Factor a perfect square on the left side: (x + 35)(x + 35) = 33325 Calculate the square root of the right side: 182.551362635 Break this problem into two subproblems by setting (x + 35) equal to 182.551362635 and -182.551362635.Subproblem 1
x + 35 = 182.551362635 Simplifying x + 35 = 182.551362635 Reorder the terms: 35 + x = 182.551362635 Solving 35 + x = 182.551362635 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 = 182.551362635 + -35 Combine like terms: 35 + -35 = 0 0 + x = 182.551362635 + -35 x = 182.551362635 + -35 Combine like terms: 182.551362635 + -35 = 147.551362635 x = 147.551362635 Simplifying x = 147.551362635Subproblem 2
x + 35 = -182.551362635 Simplifying x + 35 = -182.551362635 Reorder the terms: 35 + x = -182.551362635 Solving 35 + x = -182.551362635 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 = -182.551362635 + -35 Combine like terms: 35 + -35 = 0 0 + x = -182.551362635 + -35 x = -182.551362635 + -35 Combine like terms: -182.551362635 + -35 = -217.551362635 x = -217.551362635 Simplifying x = -217.551362635Solution
The solution to the problem is based on the solutions from the subproblems. x = {147.551362635, -217.551362635}
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