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Simplifying x2 + -12x + -1440 = 0 Reorder the terms: -1440 + -12x + x2 = 0 Solving -1440 + -12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1440' to each side of the equation. -1440 + -12x + 1440 + x2 = 0 + 1440 Reorder the terms: -1440 + 1440 + -12x + x2 = 0 + 1440 Combine like terms: -1440 + 1440 = 0 0 + -12x + x2 = 0 + 1440 -12x + x2 = 0 + 1440 Combine like terms: 0 + 1440 = 1440 -12x + x2 = 1440 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 = 1440 + 36 Reorder the terms: 36 + -12x + x2 = 1440 + 36 Combine like terms: 1440 + 36 = 1476 36 + -12x + x2 = 1476 Factor a perfect square on the left side: (x + -6)(x + -6) = 1476 Calculate the square root of the right side: 38.418745425 Break this problem into two subproblems by setting (x + -6) equal to 38.418745425 and -38.418745425.Subproblem 1
x + -6 = 38.418745425 Simplifying x + -6 = 38.418745425 Reorder the terms: -6 + x = 38.418745425 Solving -6 + x = 38.418745425 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 = 38.418745425 + 6 Combine like terms: -6 + 6 = 0 0 + x = 38.418745425 + 6 x = 38.418745425 + 6 Combine like terms: 38.418745425 + 6 = 44.418745425 x = 44.418745425 Simplifying x = 44.418745425Subproblem 2
x + -6 = -38.418745425 Simplifying x + -6 = -38.418745425 Reorder the terms: -6 + x = -38.418745425 Solving -6 + x = -38.418745425 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 = -38.418745425 + 6 Combine like terms: -6 + 6 = 0 0 + x = -38.418745425 + 6 x = -38.418745425 + 6 Combine like terms: -38.418745425 + 6 = -32.418745425 x = -32.418745425 Simplifying x = -32.418745425Solution
The solution to the problem is based on the solutions from the subproblems. x = {44.418745425, -32.418745425}
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