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Simplifying x2 + -49x + -144 = 0 Reorder the terms: -144 + -49x + x2 = 0 Solving -144 + -49x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '144' to each side of the equation. -144 + -49x + 144 + x2 = 0 + 144 Reorder the terms: -144 + 144 + -49x + x2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + -49x + x2 = 0 + 144 -49x + x2 = 0 + 144 Combine like terms: 0 + 144 = 144 -49x + x2 = 144 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 = 144 + 600.25 Reorder the terms: 600.25 + -49x + x2 = 144 + 600.25 Combine like terms: 144 + 600.25 = 744.25 600.25 + -49x + x2 = 744.25 Factor a perfect square on the left side: (x + -24.5)(x + -24.5) = 744.25 Calculate the square root of the right side: 27.280945731 Break this problem into two subproblems by setting (x + -24.5) equal to 27.280945731 and -27.280945731.Subproblem 1
x + -24.5 = 27.280945731 Simplifying x + -24.5 = 27.280945731 Reorder the terms: -24.5 + x = 27.280945731 Solving -24.5 + x = 27.280945731 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 = 27.280945731 + 24.5 Combine like terms: -24.5 + 24.5 = 0.0 0.0 + x = 27.280945731 + 24.5 x = 27.280945731 + 24.5 Combine like terms: 27.280945731 + 24.5 = 51.780945731 x = 51.780945731 Simplifying x = 51.780945731Subproblem 2
x + -24.5 = -27.280945731 Simplifying x + -24.5 = -27.280945731 Reorder the terms: -24.5 + x = -27.280945731 Solving -24.5 + x = -27.280945731 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 = -27.280945731 + 24.5 Combine like terms: -24.5 + 24.5 = 0.0 0.0 + x = -27.280945731 + 24.5 x = -27.280945731 + 24.5 Combine like terms: -27.280945731 + 24.5 = -2.780945731 x = -2.780945731 Simplifying x = -2.780945731Solution
The solution to the problem is based on the solutions from the subproblems. x = {51.780945731, -2.780945731}
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