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Simplifying x2 + 70x + -1050 = 0 Reorder the terms: -1050 + 70x + x2 = 0 Solving -1050 + 70x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1050' to each side of the equation. -1050 + 70x + 1050 + x2 = 0 + 1050 Reorder the terms: -1050 + 1050 + 70x + x2 = 0 + 1050 Combine like terms: -1050 + 1050 = 0 0 + 70x + x2 = 0 + 1050 70x + x2 = 0 + 1050 Combine like terms: 0 + 1050 = 1050 70x + x2 = 1050 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 = 1050 + 1225 Reorder the terms: 1225 + 70x + x2 = 1050 + 1225 Combine like terms: 1050 + 1225 = 2275 1225 + 70x + x2 = 2275 Factor a perfect square on the left side: (x + 35)(x + 35) = 2275 Calculate the square root of the right side: 47.696960071 Break this problem into two subproblems by setting (x + 35) equal to 47.696960071 and -47.696960071.Subproblem 1
x + 35 = 47.696960071 Simplifying x + 35 = 47.696960071 Reorder the terms: 35 + x = 47.696960071 Solving 35 + x = 47.696960071 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 = 47.696960071 + -35 Combine like terms: 35 + -35 = 0 0 + x = 47.696960071 + -35 x = 47.696960071 + -35 Combine like terms: 47.696960071 + -35 = 12.696960071 x = 12.696960071 Simplifying x = 12.696960071Subproblem 2
x + 35 = -47.696960071 Simplifying x + 35 = -47.696960071 Reorder the terms: 35 + x = -47.696960071 Solving 35 + x = -47.696960071 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 = -47.696960071 + -35 Combine like terms: 35 + -35 = 0 0 + x = -47.696960071 + -35 x = -47.696960071 + -35 Combine like terms: -47.696960071 + -35 = -82.696960071 x = -82.696960071 Simplifying x = -82.696960071Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.696960071, -82.696960071}
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