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Simplifying x(x + -100) = 4300 Reorder the terms: x(-100 + x) = 4300 (-100 * x + x * x) = 4300 (-100x + x2) = 4300 Solving -100x + x2 = 4300 Solving for variable 'x'. Reorder the terms: -4300 + -100x + x2 = 4300 + -4300 Combine like terms: 4300 + -4300 = 0 -4300 + -100x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '4300' to each side of the equation. -4300 + -100x + 4300 + x2 = 0 + 4300 Reorder the terms: -4300 + 4300 + -100x + x2 = 0 + 4300 Combine like terms: -4300 + 4300 = 0 0 + -100x + x2 = 0 + 4300 -100x + x2 = 0 + 4300 Combine like terms: 0 + 4300 = 4300 -100x + x2 = 4300 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 = 4300 + 2500 Reorder the terms: 2500 + -100x + x2 = 4300 + 2500 Combine like terms: 4300 + 2500 = 6800 2500 + -100x + x2 = 6800 Factor a perfect square on the left side: (x + -50)(x + -50) = 6800 Calculate the square root of the right side: 82.462112512 Break this problem into two subproblems by setting (x + -50) equal to 82.462112512 and -82.462112512.Subproblem 1
x + -50 = 82.462112512 Simplifying x + -50 = 82.462112512 Reorder the terms: -50 + x = 82.462112512 Solving -50 + x = 82.462112512 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 = 82.462112512 + 50 Combine like terms: -50 + 50 = 0 0 + x = 82.462112512 + 50 x = 82.462112512 + 50 Combine like terms: 82.462112512 + 50 = 132.462112512 x = 132.462112512 Simplifying x = 132.462112512Subproblem 2
x + -50 = -82.462112512 Simplifying x + -50 = -82.462112512 Reorder the terms: -50 + x = -82.462112512 Solving -50 + x = -82.462112512 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 = -82.462112512 + 50 Combine like terms: -50 + 50 = 0 0 + x = -82.462112512 + 50 x = -82.462112512 + 50 Combine like terms: -82.462112512 + 50 = -32.462112512 x = -32.462112512 Simplifying x = -32.462112512Solution
The solution to the problem is based on the solutions from the subproblems. x = {132.462112512, -32.462112512}
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