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Simplifying x2 + 700x + -17000 = 0 Reorder the terms: -17000 + 700x + x2 = 0 Solving -17000 + 700x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '17000' to each side of the equation. -17000 + 700x + 17000 + x2 = 0 + 17000 Reorder the terms: -17000 + 17000 + 700x + x2 = 0 + 17000 Combine like terms: -17000 + 17000 = 0 0 + 700x + x2 = 0 + 17000 700x + x2 = 0 + 17000 Combine like terms: 0 + 17000 = 17000 700x + x2 = 17000 The x term is 700x. Take half its coefficient (350). Square it (122500) and add it to both sides. Add '122500' to each side of the equation. 700x + 122500 + x2 = 17000 + 122500 Reorder the terms: 122500 + 700x + x2 = 17000 + 122500 Combine like terms: 17000 + 122500 = 139500 122500 + 700x + x2 = 139500 Factor a perfect square on the left side: (x + 350)(x + 350) = 139500 Calculate the square root of the right side: 373.49698794 Break this problem into two subproblems by setting (x + 350) equal to 373.49698794 and -373.49698794.Subproblem 1
x + 350 = 373.49698794 Simplifying x + 350 = 373.49698794 Reorder the terms: 350 + x = 373.49698794 Solving 350 + x = 373.49698794 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-350' to each side of the equation. 350 + -350 + x = 373.49698794 + -350 Combine like terms: 350 + -350 = 0 0 + x = 373.49698794 + -350 x = 373.49698794 + -350 Combine like terms: 373.49698794 + -350 = 23.49698794 x = 23.49698794 Simplifying x = 23.49698794Subproblem 2
x + 350 = -373.49698794 Simplifying x + 350 = -373.49698794 Reorder the terms: 350 + x = -373.49698794 Solving 350 + x = -373.49698794 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-350' to each side of the equation. 350 + -350 + x = -373.49698794 + -350 Combine like terms: 350 + -350 = 0 0 + x = -373.49698794 + -350 x = -373.49698794 + -350 Combine like terms: -373.49698794 + -350 = -723.49698794 x = -723.49698794 Simplifying x = -723.49698794Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.49698794, -723.49698794}
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