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Simplifying x2 + 156x + -572 = 0 Reorder the terms: -572 + 156x + x2 = 0 Solving -572 + 156x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '572' to each side of the equation. -572 + 156x + 572 + x2 = 0 + 572 Reorder the terms: -572 + 572 + 156x + x2 = 0 + 572 Combine like terms: -572 + 572 = 0 0 + 156x + x2 = 0 + 572 156x + x2 = 0 + 572 Combine like terms: 0 + 572 = 572 156x + x2 = 572 The x term is 156x. Take half its coefficient (78). Square it (6084) and add it to both sides. Add '6084' to each side of the equation. 156x + 6084 + x2 = 572 + 6084 Reorder the terms: 6084 + 156x + x2 = 572 + 6084 Combine like terms: 572 + 6084 = 6656 6084 + 156x + x2 = 6656 Factor a perfect square on the left side: (x + 78)(x + 78) = 6656 Calculate the square root of the right side: 81.584312217 Break this problem into two subproblems by setting (x + 78) equal to 81.584312217 and -81.584312217.Subproblem 1
x + 78 = 81.584312217 Simplifying x + 78 = 81.584312217 Reorder the terms: 78 + x = 81.584312217 Solving 78 + x = 81.584312217 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-78' to each side of the equation. 78 + -78 + x = 81.584312217 + -78 Combine like terms: 78 + -78 = 0 0 + x = 81.584312217 + -78 x = 81.584312217 + -78 Combine like terms: 81.584312217 + -78 = 3.584312217 x = 3.584312217 Simplifying x = 3.584312217Subproblem 2
x + 78 = -81.584312217 Simplifying x + 78 = -81.584312217 Reorder the terms: 78 + x = -81.584312217 Solving 78 + x = -81.584312217 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-78' to each side of the equation. 78 + -78 + x = -81.584312217 + -78 Combine like terms: 78 + -78 = 0 0 + x = -81.584312217 + -78 x = -81.584312217 + -78 Combine like terms: -81.584312217 + -78 = -159.584312217 x = -159.584312217 Simplifying x = -159.584312217Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.584312217, -159.584312217}
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