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Simplifying x2 + -156x + 1 = 0 Reorder the terms: 1 + -156x + x2 = 0 Solving 1 + -156x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -156x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -156x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -156x + x2 = 0 + -1 -156x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -156x + x2 = -1 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 = -1 + 6084 Reorder the terms: 6084 + -156x + x2 = -1 + 6084 Combine like terms: -1 + 6084 = 6083 6084 + -156x + x2 = 6083 Factor a perfect square on the left side: (x + -78)(x + -78) = 6083 Calculate the square root of the right side: 77.99358948 Break this problem into two subproblems by setting (x + -78) equal to 77.99358948 and -77.99358948.Subproblem 1
x + -78 = 77.99358948 Simplifying x + -78 = 77.99358948 Reorder the terms: -78 + x = 77.99358948 Solving -78 + x = 77.99358948 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 = 77.99358948 + 78 Combine like terms: -78 + 78 = 0 0 + x = 77.99358948 + 78 x = 77.99358948 + 78 Combine like terms: 77.99358948 + 78 = 155.99358948 x = 155.99358948 Simplifying x = 155.99358948Subproblem 2
x + -78 = -77.99358948 Simplifying x + -78 = -77.99358948 Reorder the terms: -78 + x = -77.99358948 Solving -78 + x = -77.99358948 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 = -77.99358948 + 78 Combine like terms: -78 + 78 = 0 0 + x = -77.99358948 + 78 x = -77.99358948 + 78 Combine like terms: -77.99358948 + 78 = 0.00641052 x = 0.00641052 Simplifying x = 0.00641052Solution
The solution to the problem is based on the solutions from the subproblems. x = {155.99358948, 0.00641052}
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