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Simplifying x2 + 100x = 24 Reorder the terms: 100x + x2 = 24 Solving 100x + x2 = 24 Solving for variable 'x'. Reorder the terms: -24 + 100x + x2 = 24 + -24 Combine like terms: 24 + -24 = 0 -24 + 100x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + 100x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + 100x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 100x + x2 = 0 + 24 100x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 100x + x2 = 24 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 = 24 + 2500 Reorder the terms: 2500 + 100x + x2 = 24 + 2500 Combine like terms: 24 + 2500 = 2524 2500 + 100x + x2 = 2524 Factor a perfect square on the left side: (x + 50)(x + 50) = 2524 Calculate the square root of the right side: 50.239426748 Break this problem into two subproblems by setting (x + 50) equal to 50.239426748 and -50.239426748.Subproblem 1
x + 50 = 50.239426748 Simplifying x + 50 = 50.239426748 Reorder the terms: 50 + x = 50.239426748 Solving 50 + x = 50.239426748 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 = 50.239426748 + -50 Combine like terms: 50 + -50 = 0 0 + x = 50.239426748 + -50 x = 50.239426748 + -50 Combine like terms: 50.239426748 + -50 = 0.239426748 x = 0.239426748 Simplifying x = 0.239426748Subproblem 2
x + 50 = -50.239426748 Simplifying x + 50 = -50.239426748 Reorder the terms: 50 + x = -50.239426748 Solving 50 + x = -50.239426748 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 = -50.239426748 + -50 Combine like terms: 50 + -50 = 0 0 + x = -50.239426748 + -50 x = -50.239426748 + -50 Combine like terms: -50.239426748 + -50 = -100.239426748 x = -100.239426748 Simplifying x = -100.239426748Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.239426748, -100.239426748}
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