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Simplifying x2 + 70x + -400 = 0 Reorder the terms: -400 + 70x + x2 = 0 Solving -400 + 70x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '400' to each side of the equation. -400 + 70x + 400 + x2 = 0 + 400 Reorder the terms: -400 + 400 + 70x + x2 = 0 + 400 Combine like terms: -400 + 400 = 0 0 + 70x + x2 = 0 + 400 70x + x2 = 0 + 400 Combine like terms: 0 + 400 = 400 70x + x2 = 400 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 = 400 + 1225 Reorder the terms: 1225 + 70x + x2 = 400 + 1225 Combine like terms: 400 + 1225 = 1625 1225 + 70x + x2 = 1625 Factor a perfect square on the left side: (x + 35)(x + 35) = 1625 Calculate the square root of the right side: 40.311288741 Break this problem into two subproblems by setting (x + 35) equal to 40.311288741 and -40.311288741.Subproblem 1
x + 35 = 40.311288741 Simplifying x + 35 = 40.311288741 Reorder the terms: 35 + x = 40.311288741 Solving 35 + x = 40.311288741 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 = 40.311288741 + -35 Combine like terms: 35 + -35 = 0 0 + x = 40.311288741 + -35 x = 40.311288741 + -35 Combine like terms: 40.311288741 + -35 = 5.311288741 x = 5.311288741 Simplifying x = 5.311288741Subproblem 2
x + 35 = -40.311288741 Simplifying x + 35 = -40.311288741 Reorder the terms: 35 + x = -40.311288741 Solving 35 + x = -40.311288741 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 = -40.311288741 + -35 Combine like terms: 35 + -35 = 0 0 + x = -40.311288741 + -35 x = -40.311288741 + -35 Combine like terms: -40.311288741 + -35 = -75.311288741 x = -75.311288741 Simplifying x = -75.311288741Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.311288741, -75.311288741}
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