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Simplifying x2 + 100x = 7 Reorder the terms: 100x + x2 = 7 Solving 100x + x2 = 7 Solving for variable 'x'. Reorder the terms: -7 + 100x + x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + 100x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + 100x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + 100x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 100x + x2 = 0 + 7 100x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 100x + x2 = 7 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 = 7 + 2500 Reorder the terms: 2500 + 100x + x2 = 7 + 2500 Combine like terms: 7 + 2500 = 2507 2500 + 100x + x2 = 2507 Factor a perfect square on the left side: (x + 50)(x + 50) = 2507 Calculate the square root of the right side: 50.069951068 Break this problem into two subproblems by setting (x + 50) equal to 50.069951068 and -50.069951068.Subproblem 1
x + 50 = 50.069951068 Simplifying x + 50 = 50.069951068 Reorder the terms: 50 + x = 50.069951068 Solving 50 + x = 50.069951068 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 = 50.069951068 + -50 Combine like terms: 50 + -50 = 0 0 + x = 50.069951068 + -50 x = 50.069951068 + -50 Combine like terms: 50.069951068 + -50 = 0.069951068 x = 0.069951068 Simplifying x = 0.069951068Subproblem 2
x + 50 = -50.069951068 Simplifying x + 50 = -50.069951068 Reorder the terms: 50 + x = -50.069951068 Solving 50 + x = -50.069951068 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 = -50.069951068 + -50 Combine like terms: 50 + -50 = 0 0 + x = -50.069951068 + -50 x = -50.069951068 + -50 Combine like terms: -50.069951068 + -50 = -100.069951068 x = -100.069951068 Simplifying x = -100.069951068Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.069951068, -100.069951068}
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