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Simplifying x2 + -6x + -15624 = 0 Reorder the terms: -15624 + -6x + x2 = 0 Solving -15624 + -6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '15624' to each side of the equation. -15624 + -6x + 15624 + x2 = 0 + 15624 Reorder the terms: -15624 + 15624 + -6x + x2 = 0 + 15624 Combine like terms: -15624 + 15624 = 0 0 + -6x + x2 = 0 + 15624 -6x + x2 = 0 + 15624 Combine like terms: 0 + 15624 = 15624 -6x + x2 = 15624 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 15624 + 9 Reorder the terms: 9 + -6x + x2 = 15624 + 9 Combine like terms: 15624 + 9 = 15633 9 + -6x + x2 = 15633 Factor a perfect square on the left side: (x + -3)(x + -3) = 15633 Calculate the square root of the right side: 125.031995905 Break this problem into two subproblems by setting (x + -3) equal to 125.031995905 and -125.031995905.Subproblem 1
x + -3 = 125.031995905 Simplifying x + -3 = 125.031995905 Reorder the terms: -3 + x = 125.031995905 Solving -3 + x = 125.031995905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 125.031995905 + 3 Combine like terms: -3 + 3 = 0 0 + x = 125.031995905 + 3 x = 125.031995905 + 3 Combine like terms: 125.031995905 + 3 = 128.031995905 x = 128.031995905 Simplifying x = 128.031995905Subproblem 2
x + -3 = -125.031995905 Simplifying x + -3 = -125.031995905 Reorder the terms: -3 + x = -125.031995905 Solving -3 + x = -125.031995905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -125.031995905 + 3 Combine like terms: -3 + 3 = 0 0 + x = -125.031995905 + 3 x = -125.031995905 + 3 Combine like terms: -125.031995905 + 3 = -122.031995905 x = -122.031995905 Simplifying x = -122.031995905Solution
The solution to the problem is based on the solutions from the subproblems. x = {128.031995905, -122.031995905}
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