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Simplifying x2 + -24x + -80 = 0 Reorder the terms: -80 + -24x + x2 = 0 Solving -80 + -24x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '80' to each side of the equation. -80 + -24x + 80 + x2 = 0 + 80 Reorder the terms: -80 + 80 + -24x + x2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + -24x + x2 = 0 + 80 -24x + x2 = 0 + 80 Combine like terms: 0 + 80 = 80 -24x + x2 = 80 The x term is -24x. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24x + 144 + x2 = 80 + 144 Reorder the terms: 144 + -24x + x2 = 80 + 144 Combine like terms: 80 + 144 = 224 144 + -24x + x2 = 224 Factor a perfect square on the left side: (x + -12)(x + -12) = 224 Calculate the square root of the right side: 14.966629547 Break this problem into two subproblems by setting (x + -12) equal to 14.966629547 and -14.966629547.Subproblem 1
x + -12 = 14.966629547 Simplifying x + -12 = 14.966629547 Reorder the terms: -12 + x = 14.966629547 Solving -12 + x = 14.966629547 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 14.966629547 + 12 Combine like terms: -12 + 12 = 0 0 + x = 14.966629547 + 12 x = 14.966629547 + 12 Combine like terms: 14.966629547 + 12 = 26.966629547 x = 26.966629547 Simplifying x = 26.966629547Subproblem 2
x + -12 = -14.966629547 Simplifying x + -12 = -14.966629547 Reorder the terms: -12 + x = -14.966629547 Solving -12 + x = -14.966629547 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -14.966629547 + 12 Combine like terms: -12 + 12 = 0 0 + x = -14.966629547 + 12 x = -14.966629547 + 12 Combine like terms: -14.966629547 + 12 = -2.966629547 x = -2.966629547 Simplifying x = -2.966629547Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.966629547, -2.966629547}
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