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Simplifying x(x + 49) = 14 Reorder the terms: x(49 + x) = 14 (49 * x + x * x) = 14 (49x + x2) = 14 Solving 49x + x2 = 14 Solving for variable 'x'. Reorder the terms: -14 + 49x + x2 = 14 + -14 Combine like terms: 14 + -14 = 0 -14 + 49x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + 49x + 14 + x2 = 0 + 14 Reorder the terms: -14 + 14 + 49x + x2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 49x + x2 = 0 + 14 49x + x2 = 0 + 14 Combine like terms: 0 + 14 = 14 49x + x2 = 14 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 = 14 + 600.25 Reorder the terms: 600.25 + 49x + x2 = 14 + 600.25 Combine like terms: 14 + 600.25 = 614.25 600.25 + 49x + x2 = 614.25 Factor a perfect square on the left side: (x + 24.5)(x + 24.5) = 614.25 Calculate the square root of the right side: 24.784067463 Break this problem into two subproblems by setting (x + 24.5) equal to 24.784067463 and -24.784067463.Subproblem 1
x + 24.5 = 24.784067463 Simplifying x + 24.5 = 24.784067463 Reorder the terms: 24.5 + x = 24.784067463 Solving 24.5 + x = 24.784067463 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 = 24.784067463 + -24.5 Combine like terms: 24.5 + -24.5 = 0.0 0.0 + x = 24.784067463 + -24.5 x = 24.784067463 + -24.5 Combine like terms: 24.784067463 + -24.5 = 0.284067463 x = 0.284067463 Simplifying x = 0.284067463Subproblem 2
x + 24.5 = -24.784067463 Simplifying x + 24.5 = -24.784067463 Reorder the terms: 24.5 + x = -24.784067463 Solving 24.5 + x = -24.784067463 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 = -24.784067463 + -24.5 Combine like terms: 24.5 + -24.5 = 0.0 0.0 + x = -24.784067463 + -24.5 x = -24.784067463 + -24.5 Combine like terms: -24.784067463 + -24.5 = -49.284067463 x = -49.284067463 Simplifying x = -49.284067463Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.284067463, -49.284067463}
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