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Simplifying x2 + -49x + -328 = 0 Reorder the terms: -328 + -49x + x2 = 0 Solving -328 + -49x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '328' to each side of the equation. -328 + -49x + 328 + x2 = 0 + 328 Reorder the terms: -328 + 328 + -49x + x2 = 0 + 328 Combine like terms: -328 + 328 = 0 0 + -49x + x2 = 0 + 328 -49x + x2 = 0 + 328 Combine like terms: 0 + 328 = 328 -49x + x2 = 328 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 = 328 + 600.25 Reorder the terms: 600.25 + -49x + x2 = 328 + 600.25 Combine like terms: 328 + 600.25 = 928.25 600.25 + -49x + x2 = 928.25 Factor a perfect square on the left side: (x + -24.5)(x + -24.5) = 928.25 Calculate the square root of the right side: 30.467195473 Break this problem into two subproblems by setting (x + -24.5) equal to 30.467195473 and -30.467195473.Subproblem 1
x + -24.5 = 30.467195473 Simplifying x + -24.5 = 30.467195473 Reorder the terms: -24.5 + x = 30.467195473 Solving -24.5 + x = 30.467195473 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 = 30.467195473 + 24.5 Combine like terms: -24.5 + 24.5 = 0.0 0.0 + x = 30.467195473 + 24.5 x = 30.467195473 + 24.5 Combine like terms: 30.467195473 + 24.5 = 54.967195473 x = 54.967195473 Simplifying x = 54.967195473Subproblem 2
x + -24.5 = -30.467195473 Simplifying x + -24.5 = -30.467195473 Reorder the terms: -24.5 + x = -30.467195473 Solving -24.5 + x = -30.467195473 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 = -30.467195473 + 24.5 Combine like terms: -24.5 + 24.5 = 0.0 0.0 + x = -30.467195473 + 24.5 x = -30.467195473 + 24.5 Combine like terms: -30.467195473 + 24.5 = -5.967195473 x = -5.967195473 Simplifying x = -5.967195473Solution
The solution to the problem is based on the solutions from the subproblems. x = {54.967195473, -5.967195473}
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