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Simplifying X2 + -24X = 144 Reorder the terms: -24X + X2 = 144 Solving -24X + X2 = 144 Solving for variable 'X'. Reorder the terms: -144 + -24X + X2 = 144 + -144 Combine like terms: 144 + -144 = 0 -144 + -24X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '144' to each side of the equation. -144 + -24X + 144 + X2 = 0 + 144 Reorder the terms: -144 + 144 + -24X + X2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + -24X + X2 = 0 + 144 -24X + X2 = 0 + 144 Combine like terms: 0 + 144 = 144 -24X + X2 = 144 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 = 144 + 144 Reorder the terms: 144 + -24X + X2 = 144 + 144 Combine like terms: 144 + 144 = 288 144 + -24X + X2 = 288 Factor a perfect square on the left side: (X + -12)(X + -12) = 288 Calculate the square root of the right side: 16.970562748 Break this problem into two subproblems by setting (X + -12) equal to 16.970562748 and -16.970562748.Subproblem 1
X + -12 = 16.970562748 Simplifying X + -12 = 16.970562748 Reorder the terms: -12 + X = 16.970562748 Solving -12 + X = 16.970562748 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 = 16.970562748 + 12 Combine like terms: -12 + 12 = 0 0 + X = 16.970562748 + 12 X = 16.970562748 + 12 Combine like terms: 16.970562748 + 12 = 28.970562748 X = 28.970562748 Simplifying X = 28.970562748Subproblem 2
X + -12 = -16.970562748 Simplifying X + -12 = -16.970562748 Reorder the terms: -12 + X = -16.970562748 Solving -12 + X = -16.970562748 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 = -16.970562748 + 12 Combine like terms: -12 + 12 = 0 0 + X = -16.970562748 + 12 X = -16.970562748 + 12 Combine like terms: -16.970562748 + 12 = -4.970562748 X = -4.970562748 Simplifying X = -4.970562748Solution
The solution to the problem is based on the solutions from the subproblems. X = {28.970562748, -4.970562748}
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