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Simplifying x2 + 70x + -300 = 0 Reorder the terms: -300 + 70x + x2 = 0 Solving -300 + 70x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '300' to each side of the equation. -300 + 70x + 300 + x2 = 0 + 300 Reorder the terms: -300 + 300 + 70x + x2 = 0 + 300 Combine like terms: -300 + 300 = 0 0 + 70x + x2 = 0 + 300 70x + x2 = 0 + 300 Combine like terms: 0 + 300 = 300 70x + x2 = 300 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 = 300 + 1225 Reorder the terms: 1225 + 70x + x2 = 300 + 1225 Combine like terms: 300 + 1225 = 1525 1225 + 70x + x2 = 1525 Factor a perfect square on the left side: (x + 35)(x + 35) = 1525 Calculate the square root of the right side: 39.05124838 Break this problem into two subproblems by setting (x + 35) equal to 39.05124838 and -39.05124838.Subproblem 1
x + 35 = 39.05124838 Simplifying x + 35 = 39.05124838 Reorder the terms: 35 + x = 39.05124838 Solving 35 + x = 39.05124838 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 = 39.05124838 + -35 Combine like terms: 35 + -35 = 0 0 + x = 39.05124838 + -35 x = 39.05124838 + -35 Combine like terms: 39.05124838 + -35 = 4.05124838 x = 4.05124838 Simplifying x = 4.05124838Subproblem 2
x + 35 = -39.05124838 Simplifying x + 35 = -39.05124838 Reorder the terms: 35 + x = -39.05124838 Solving 35 + x = -39.05124838 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 = -39.05124838 + -35 Combine like terms: 35 + -35 = 0 0 + x = -39.05124838 + -35 x = -39.05124838 + -35 Combine like terms: -39.05124838 + -35 = -74.05124838 x = -74.05124838 Simplifying x = -74.05124838Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.05124838, -74.05124838}
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