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Simplifying x2 + 43x = 175 Reorder the terms: 43x + x2 = 175 Solving 43x + x2 = 175 Solving for variable 'x'. Reorder the terms: -175 + 43x + x2 = 175 + -175 Combine like terms: 175 + -175 = 0 -175 + 43x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '175' to each side of the equation. -175 + 43x + 175 + x2 = 0 + 175 Reorder the terms: -175 + 175 + 43x + x2 = 0 + 175 Combine like terms: -175 + 175 = 0 0 + 43x + x2 = 0 + 175 43x + x2 = 0 + 175 Combine like terms: 0 + 175 = 175 43x + x2 = 175 The x term is 43x. Take half its coefficient (21.5). Square it (462.25) and add it to both sides. Add '462.25' to each side of the equation. 43x + 462.25 + x2 = 175 + 462.25 Reorder the terms: 462.25 + 43x + x2 = 175 + 462.25 Combine like terms: 175 + 462.25 = 637.25 462.25 + 43x + x2 = 637.25 Factor a perfect square on the left side: (x + 21.5)(x + 21.5) = 637.25 Calculate the square root of the right side: 25.243811123 Break this problem into two subproblems by setting (x + 21.5) equal to 25.243811123 and -25.243811123.Subproblem 1
x + 21.5 = 25.243811123 Simplifying x + 21.5 = 25.243811123 Reorder the terms: 21.5 + x = 25.243811123 Solving 21.5 + x = 25.243811123 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-21.5' to each side of the equation. 21.5 + -21.5 + x = 25.243811123 + -21.5 Combine like terms: 21.5 + -21.5 = 0.0 0.0 + x = 25.243811123 + -21.5 x = 25.243811123 + -21.5 Combine like terms: 25.243811123 + -21.5 = 3.743811123 x = 3.743811123 Simplifying x = 3.743811123Subproblem 2
x + 21.5 = -25.243811123 Simplifying x + 21.5 = -25.243811123 Reorder the terms: 21.5 + x = -25.243811123 Solving 21.5 + x = -25.243811123 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-21.5' to each side of the equation. 21.5 + -21.5 + x = -25.243811123 + -21.5 Combine like terms: 21.5 + -21.5 = 0.0 0.0 + x = -25.243811123 + -21.5 x = -25.243811123 + -21.5 Combine like terms: -25.243811123 + -21.5 = -46.743811123 x = -46.743811123 Simplifying x = -46.743811123Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.743811123, -46.743811123}
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