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Simplifying x2 + 4x + -1472 = 0 Reorder the terms: -1472 + 4x + x2 = 0 Solving -1472 + 4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1472' to each side of the equation. -1472 + 4x + 1472 + x2 = 0 + 1472 Reorder the terms: -1472 + 1472 + 4x + x2 = 0 + 1472 Combine like terms: -1472 + 1472 = 0 0 + 4x + x2 = 0 + 1472 4x + x2 = 0 + 1472 Combine like terms: 0 + 1472 = 1472 4x + x2 = 1472 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 1472 + 4 Reorder the terms: 4 + 4x + x2 = 1472 + 4 Combine like terms: 1472 + 4 = 1476 4 + 4x + x2 = 1476 Factor a perfect square on the left side: (x + 2)(x + 2) = 1476 Calculate the square root of the right side: 38.418745425 Break this problem into two subproblems by setting (x + 2) equal to 38.418745425 and -38.418745425.Subproblem 1
x + 2 = 38.418745425 Simplifying x + 2 = 38.418745425 Reorder the terms: 2 + x = 38.418745425 Solving 2 + x = 38.418745425 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 38.418745425 + -2 Combine like terms: 2 + -2 = 0 0 + x = 38.418745425 + -2 x = 38.418745425 + -2 Combine like terms: 38.418745425 + -2 = 36.418745425 x = 36.418745425 Simplifying x = 36.418745425Subproblem 2
x + 2 = -38.418745425 Simplifying x + 2 = -38.418745425 Reorder the terms: 2 + x = -38.418745425 Solving 2 + x = -38.418745425 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -38.418745425 + -2 Combine like terms: 2 + -2 = 0 0 + x = -38.418745425 + -2 x = -38.418745425 + -2 Combine like terms: -38.418745425 + -2 = -40.418745425 x = -40.418745425 Simplifying x = -40.418745425Solution
The solution to the problem is based on the solutions from the subproblems. x = {36.418745425, -40.418745425}
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