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Simplifying x2 + -12x = 336 Reorder the terms: -12x + x2 = 336 Solving -12x + x2 = 336 Solving for variable 'x'. Reorder the terms: -336 + -12x + x2 = 336 + -336 Combine like terms: 336 + -336 = 0 -336 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '336' to each side of the equation. -336 + -12x + 336 + x2 = 0 + 336 Reorder the terms: -336 + 336 + -12x + x2 = 0 + 336 Combine like terms: -336 + 336 = 0 0 + -12x + x2 = 0 + 336 -12x + x2 = 0 + 336 Combine like terms: 0 + 336 = 336 -12x + x2 = 336 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 336 + 36 Reorder the terms: 36 + -12x + x2 = 336 + 36 Combine like terms: 336 + 36 = 372 36 + -12x + x2 = 372 Factor a perfect square on the left side: (x + -6)(x + -6) = 372 Calculate the square root of the right side: 19.287301522 Break this problem into two subproblems by setting (x + -6) equal to 19.287301522 and -19.287301522.Subproblem 1
x + -6 = 19.287301522 Simplifying x + -6 = 19.287301522 Reorder the terms: -6 + x = 19.287301522 Solving -6 + x = 19.287301522 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 19.287301522 + 6 Combine like terms: -6 + 6 = 0 0 + x = 19.287301522 + 6 x = 19.287301522 + 6 Combine like terms: 19.287301522 + 6 = 25.287301522 x = 25.287301522 Simplifying x = 25.287301522Subproblem 2
x + -6 = -19.287301522 Simplifying x + -6 = -19.287301522 Reorder the terms: -6 + x = -19.287301522 Solving -6 + x = -19.287301522 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -19.287301522 + 6 Combine like terms: -6 + 6 = 0 0 + x = -19.287301522 + 6 x = -19.287301522 + 6 Combine like terms: -19.287301522 + 6 = -13.287301522 x = -13.287301522 Simplifying x = -13.287301522Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.287301522, -13.287301522}
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