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Simplifying x2 + -700x + 1400 = 0 Reorder the terms: 1400 + -700x + x2 = 0 Solving 1400 + -700x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1400' to each side of the equation. 1400 + -700x + -1400 + x2 = 0 + -1400 Reorder the terms: 1400 + -1400 + -700x + x2 = 0 + -1400 Combine like terms: 1400 + -1400 = 0 0 + -700x + x2 = 0 + -1400 -700x + x2 = 0 + -1400 Combine like terms: 0 + -1400 = -1400 -700x + x2 = -1400 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 = -1400 + 122500 Reorder the terms: 122500 + -700x + x2 = -1400 + 122500 Combine like terms: -1400 + 122500 = 121100 122500 + -700x + x2 = 121100 Factor a perfect square on the left side: (x + -350)(x + -350) = 121100 Calculate the square root of the right side: 347.994252826 Break this problem into two subproblems by setting (x + -350) equal to 347.994252826 and -347.994252826.Subproblem 1
x + -350 = 347.994252826 Simplifying x + -350 = 347.994252826 Reorder the terms: -350 + x = 347.994252826 Solving -350 + x = 347.994252826 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 = 347.994252826 + 350 Combine like terms: -350 + 350 = 0 0 + x = 347.994252826 + 350 x = 347.994252826 + 350 Combine like terms: 347.994252826 + 350 = 697.994252826 x = 697.994252826 Simplifying x = 697.994252826Subproblem 2
x + -350 = -347.994252826 Simplifying x + -350 = -347.994252826 Reorder the terms: -350 + x = -347.994252826 Solving -350 + x = -347.994252826 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 = -347.994252826 + 350 Combine like terms: -350 + 350 = 0 0 + x = -347.994252826 + 350 x = -347.994252826 + 350 Combine like terms: -347.994252826 + 350 = 2.005747174 x = 2.005747174 Simplifying x = 2.005747174Solution
The solution to the problem is based on the solutions from the subproblems. x = {697.994252826, 2.005747174}
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