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Simplifying x2 + -49x + -185 = 0 Reorder the terms: -185 + -49x + x2 = 0 Solving -185 + -49x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '185' to each side of the equation. -185 + -49x + 185 + x2 = 0 + 185 Reorder the terms: -185 + 185 + -49x + x2 = 0 + 185 Combine like terms: -185 + 185 = 0 0 + -49x + x2 = 0 + 185 -49x + x2 = 0 + 185 Combine like terms: 0 + 185 = 185 -49x + x2 = 185 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 = 185 + 600.25 Reorder the terms: 600.25 + -49x + x2 = 185 + 600.25 Combine like terms: 185 + 600.25 = 785.25 600.25 + -49x + x2 = 785.25 Factor a perfect square on the left side: (x + -24.5)(x + -24.5) = 785.25 Calculate the square root of the right side: 28.022312538 Break this problem into two subproblems by setting (x + -24.5) equal to 28.022312538 and -28.022312538.Subproblem 1
x + -24.5 = 28.022312538 Simplifying x + -24.5 = 28.022312538 Reorder the terms: -24.5 + x = 28.022312538 Solving -24.5 + x = 28.022312538 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 = 28.022312538 + 24.5 Combine like terms: -24.5 + 24.5 = 0.0 0.0 + x = 28.022312538 + 24.5 x = 28.022312538 + 24.5 Combine like terms: 28.022312538 + 24.5 = 52.522312538 x = 52.522312538 Simplifying x = 52.522312538Subproblem 2
x + -24.5 = -28.022312538 Simplifying x + -24.5 = -28.022312538 Reorder the terms: -24.5 + x = -28.022312538 Solving -24.5 + x = -28.022312538 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 = -28.022312538 + 24.5 Combine like terms: -24.5 + 24.5 = 0.0 0.0 + x = -28.022312538 + 24.5 x = -28.022312538 + 24.5 Combine like terms: -28.022312538 + 24.5 = -3.522312538 x = -3.522312538 Simplifying x = -3.522312538Solution
The solution to the problem is based on the solutions from the subproblems. x = {52.522312538, -3.522312538}
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