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Simplifying 225 = x2 + -16x + 68 Reorder the terms: 225 = 68 + -16x + x2 Solving 225 = 68 + -16x + x2 Solving for variable 'x'. Combine like terms: 225 + -68 = 157 157 + 16x + -1x2 = 68 + -16x + x2 + -68 + 16x + -1x2 Reorder the terms: 157 + 16x + -1x2 = 68 + -68 + -16x + 16x + x2 + -1x2 Combine like terms: 68 + -68 = 0 157 + 16x + -1x2 = 0 + -16x + 16x + x2 + -1x2 157 + 16x + -1x2 = -16x + 16x + x2 + -1x2 Combine like terms: -16x + 16x = 0 157 + 16x + -1x2 = 0 + x2 + -1x2 157 + 16x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 157 + 16x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -157 + -16x + x2 = 0 Move the constant term to the right: Add '157' to each side of the equation. -157 + -16x + 157 + x2 = 0 + 157 Reorder the terms: -157 + 157 + -16x + x2 = 0 + 157 Combine like terms: -157 + 157 = 0 0 + -16x + x2 = 0 + 157 -16x + x2 = 0 + 157 Combine like terms: 0 + 157 = 157 -16x + x2 = 157 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = 157 + 64 Reorder the terms: 64 + -16x + x2 = 157 + 64 Combine like terms: 157 + 64 = 221 64 + -16x + x2 = 221 Factor a perfect square on the left side: (x + -8)(x + -8) = 221 Calculate the square root of the right side: 14.866068747 Break this problem into two subproblems by setting (x + -8) equal to 14.866068747 and -14.866068747.Subproblem 1
x + -8 = 14.866068747 Simplifying x + -8 = 14.866068747 Reorder the terms: -8 + x = 14.866068747 Solving -8 + x = 14.866068747 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 14.866068747 + 8 Combine like terms: -8 + 8 = 0 0 + x = 14.866068747 + 8 x = 14.866068747 + 8 Combine like terms: 14.866068747 + 8 = 22.866068747 x = 22.866068747 Simplifying x = 22.866068747Subproblem 2
x + -8 = -14.866068747 Simplifying x + -8 = -14.866068747 Reorder the terms: -8 + x = -14.866068747 Solving -8 + x = -14.866068747 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -14.866068747 + 8 Combine like terms: -8 + 8 = 0 0 + x = -14.866068747 + 8 x = -14.866068747 + 8 Combine like terms: -14.866068747 + 8 = -6.866068747 x = -6.866068747 Simplifying x = -6.866068747Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.866068747, -6.866068747}
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