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Simplifying x2 + 70x + -8040 = 0 Reorder the terms: -8040 + 70x + x2 = 0 Solving -8040 + 70x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '8040' to each side of the equation. -8040 + 70x + 8040 + x2 = 0 + 8040 Reorder the terms: -8040 + 8040 + 70x + x2 = 0 + 8040 Combine like terms: -8040 + 8040 = 0 0 + 70x + x2 = 0 + 8040 70x + x2 = 0 + 8040 Combine like terms: 0 + 8040 = 8040 70x + x2 = 8040 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 = 8040 + 1225 Reorder the terms: 1225 + 70x + x2 = 8040 + 1225 Combine like terms: 8040 + 1225 = 9265 1225 + 70x + x2 = 9265 Factor a perfect square on the left side: (x + 35)(x + 35) = 9265 Calculate the square root of the right side: 96.254870007 Break this problem into two subproblems by setting (x + 35) equal to 96.254870007 and -96.254870007.Subproblem 1
x + 35 = 96.254870007 Simplifying x + 35 = 96.254870007 Reorder the terms: 35 + x = 96.254870007 Solving 35 + x = 96.254870007 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 = 96.254870007 + -35 Combine like terms: 35 + -35 = 0 0 + x = 96.254870007 + -35 x = 96.254870007 + -35 Combine like terms: 96.254870007 + -35 = 61.254870007 x = 61.254870007 Simplifying x = 61.254870007Subproblem 2
x + 35 = -96.254870007 Simplifying x + 35 = -96.254870007 Reorder the terms: 35 + x = -96.254870007 Solving 35 + x = -96.254870007 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 = -96.254870007 + -35 Combine like terms: 35 + -35 = 0 0 + x = -96.254870007 + -35 x = -96.254870007 + -35 Combine like terms: -96.254870007 + -35 = -131.254870007 x = -131.254870007 Simplifying x = -131.254870007Solution
The solution to the problem is based on the solutions from the subproblems. x = {61.254870007, -131.254870007}
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