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Simplifying x2 + 100x + -700 = 0 Reorder the terms: -700 + 100x + x2 = 0 Solving -700 + 100x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '700' to each side of the equation. -700 + 100x + 700 + x2 = 0 + 700 Reorder the terms: -700 + 700 + 100x + x2 = 0 + 700 Combine like terms: -700 + 700 = 0 0 + 100x + x2 = 0 + 700 100x + x2 = 0 + 700 Combine like terms: 0 + 700 = 700 100x + x2 = 700 The x term is 100x. Take half its coefficient (50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. 100x + 2500 + x2 = 700 + 2500 Reorder the terms: 2500 + 100x + x2 = 700 + 2500 Combine like terms: 700 + 2500 = 3200 2500 + 100x + x2 = 3200 Factor a perfect square on the left side: (x + 50)(x + 50) = 3200 Calculate the square root of the right side: 56.568542495 Break this problem into two subproblems by setting (x + 50) equal to 56.568542495 and -56.568542495.Subproblem 1
x + 50 = 56.568542495 Simplifying x + 50 = 56.568542495 Reorder the terms: 50 + x = 56.568542495 Solving 50 + x = 56.568542495 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + x = 56.568542495 + -50 Combine like terms: 50 + -50 = 0 0 + x = 56.568542495 + -50 x = 56.568542495 + -50 Combine like terms: 56.568542495 + -50 = 6.568542495 x = 6.568542495 Simplifying x = 6.568542495Subproblem 2
x + 50 = -56.568542495 Simplifying x + 50 = -56.568542495 Reorder the terms: 50 + x = -56.568542495 Solving 50 + x = -56.568542495 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + x = -56.568542495 + -50 Combine like terms: 50 + -50 = 0 0 + x = -56.568542495 + -50 x = -56.568542495 + -50 Combine like terms: -56.568542495 + -50 = -106.568542495 x = -106.568542495 Simplifying x = -106.568542495Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.568542495, -106.568542495}
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