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Simplifying x2 + 95x + 2100 = 375 Reorder the terms: 2100 + 95x + x2 = 375 Solving 2100 + 95x + x2 = 375 Solving for variable 'x'. Reorder the terms: 2100 + -375 + 95x + x2 = 375 + -375 Combine like terms: 2100 + -375 = 1725 1725 + 95x + x2 = 375 + -375 Combine like terms: 375 + -375 = 0 1725 + 95x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1725' to each side of the equation. 1725 + 95x + -1725 + x2 = 0 + -1725 Reorder the terms: 1725 + -1725 + 95x + x2 = 0 + -1725 Combine like terms: 1725 + -1725 = 0 0 + 95x + x2 = 0 + -1725 95x + x2 = 0 + -1725 Combine like terms: 0 + -1725 = -1725 95x + x2 = -1725 The x term is 95x. Take half its coefficient (47.5). Square it (2256.25) and add it to both sides. Add '2256.25' to each side of the equation. 95x + 2256.25 + x2 = -1725 + 2256.25 Reorder the terms: 2256.25 + 95x + x2 = -1725 + 2256.25 Combine like terms: -1725 + 2256.25 = 531.25 2256.25 + 95x + x2 = 531.25 Factor a perfect square on the left side: (x + 47.5)(x + 47.5) = 531.25 Calculate the square root of the right side: 23.048861143 Break this problem into two subproblems by setting (x + 47.5) equal to 23.048861143 and -23.048861143.Subproblem 1
x + 47.5 = 23.048861143 Simplifying x + 47.5 = 23.048861143 Reorder the terms: 47.5 + x = 23.048861143 Solving 47.5 + x = 23.048861143 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-47.5' to each side of the equation. 47.5 + -47.5 + x = 23.048861143 + -47.5 Combine like terms: 47.5 + -47.5 = 0.0 0.0 + x = 23.048861143 + -47.5 x = 23.048861143 + -47.5 Combine like terms: 23.048861143 + -47.5 = -24.451138857 x = -24.451138857 Simplifying x = -24.451138857Subproblem 2
x + 47.5 = -23.048861143 Simplifying x + 47.5 = -23.048861143 Reorder the terms: 47.5 + x = -23.048861143 Solving 47.5 + x = -23.048861143 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-47.5' to each side of the equation. 47.5 + -47.5 + x = -23.048861143 + -47.5 Combine like terms: 47.5 + -47.5 = 0.0 0.0 + x = -23.048861143 + -47.5 x = -23.048861143 + -47.5 Combine like terms: -23.048861143 + -47.5 = -70.548861143 x = -70.548861143 Simplifying x = -70.548861143Solution
The solution to the problem is based on the solutions from the subproblems. x = {-24.451138857, -70.548861143}
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