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Simplifying x(x + 49) = 435 Reorder the terms: x(49 + x) = 435 (49 * x + x * x) = 435 (49x + x2) = 435 Solving 49x + x2 = 435 Solving for variable 'x'. Reorder the terms: -435 + 49x + x2 = 435 + -435 Combine like terms: 435 + -435 = 0 -435 + 49x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '435' to each side of the equation. -435 + 49x + 435 + x2 = 0 + 435 Reorder the terms: -435 + 435 + 49x + x2 = 0 + 435 Combine like terms: -435 + 435 = 0 0 + 49x + x2 = 0 + 435 49x + x2 = 0 + 435 Combine like terms: 0 + 435 = 435 49x + x2 = 435 The x term is 49x. Take half its coefficient (24.5). Square it (600.25) and add it to both sides. Add '600.25' to each side of the equation. 49x + 600.25 + x2 = 435 + 600.25 Reorder the terms: 600.25 + 49x + x2 = 435 + 600.25 Combine like terms: 435 + 600.25 = 1035.25 600.25 + 49x + x2 = 1035.25 Factor a perfect square on the left side: (x + 24.5)(x + 24.5) = 1035.25 Calculate the square root of the right side: 32.175301086 Break this problem into two subproblems by setting (x + 24.5) equal to 32.175301086 and -32.175301086.Subproblem 1
x + 24.5 = 32.175301086 Simplifying x + 24.5 = 32.175301086 Reorder the terms: 24.5 + x = 32.175301086 Solving 24.5 + x = 32.175301086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-24.5' to each side of the equation. 24.5 + -24.5 + x = 32.175301086 + -24.5 Combine like terms: 24.5 + -24.5 = 0.0 0.0 + x = 32.175301086 + -24.5 x = 32.175301086 + -24.5 Combine like terms: 32.175301086 + -24.5 = 7.675301086 x = 7.675301086 Simplifying x = 7.675301086Subproblem 2
x + 24.5 = -32.175301086 Simplifying x + 24.5 = -32.175301086 Reorder the terms: 24.5 + x = -32.175301086 Solving 24.5 + x = -32.175301086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-24.5' to each side of the equation. 24.5 + -24.5 + x = -32.175301086 + -24.5 Combine like terms: 24.5 + -24.5 = 0.0 0.0 + x = -32.175301086 + -24.5 x = -32.175301086 + -24.5 Combine like terms: -32.175301086 + -24.5 = -56.675301086 x = -56.675301086 Simplifying x = -56.675301086Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.675301086, -56.675301086}
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