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Simplifying x2 + -24x + -396 = 0 Reorder the terms: -396 + -24x + x2 = 0 Solving -396 + -24x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '396' to each side of the equation. -396 + -24x + 396 + x2 = 0 + 396 Reorder the terms: -396 + 396 + -24x + x2 = 0 + 396 Combine like terms: -396 + 396 = 0 0 + -24x + x2 = 0 + 396 -24x + x2 = 0 + 396 Combine like terms: 0 + 396 = 396 -24x + x2 = 396 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 = 396 + 144 Reorder the terms: 144 + -24x + x2 = 396 + 144 Combine like terms: 396 + 144 = 540 144 + -24x + x2 = 540 Factor a perfect square on the left side: (x + -12)(x + -12) = 540 Calculate the square root of the right side: 23.237900077 Break this problem into two subproblems by setting (x + -12) equal to 23.237900077 and -23.237900077.Subproblem 1
x + -12 = 23.237900077 Simplifying x + -12 = 23.237900077 Reorder the terms: -12 + x = 23.237900077 Solving -12 + x = 23.237900077 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 = 23.237900077 + 12 Combine like terms: -12 + 12 = 0 0 + x = 23.237900077 + 12 x = 23.237900077 + 12 Combine like terms: 23.237900077 + 12 = 35.237900077 x = 35.237900077 Simplifying x = 35.237900077Subproblem 2
x + -12 = -23.237900077 Simplifying x + -12 = -23.237900077 Reorder the terms: -12 + x = -23.237900077 Solving -12 + x = -23.237900077 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 = -23.237900077 + 12 Combine like terms: -12 + 12 = 0 0 + x = -23.237900077 + 12 x = -23.237900077 + 12 Combine like terms: -23.237900077 + 12 = -11.237900077 x = -11.237900077 Simplifying x = -11.237900077Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.237900077, -11.237900077}
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