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Simplifying 21 = x2 + -16x + 0 Reorder the terms: 21 = 0 + -16x + x2 Remove the zero: 21 = -16x + x2 Solving 21 = -16x + x2 Solving for variable 'x'. Reorder the terms: 21 + 16x + -1x2 = -16x + 16x + x2 + -1x2 Combine like terms: -16x + 16x = 0 21 + 16x + -1x2 = 0 + x2 + -1x2 21 + 16x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 21 + 16x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -21 + -16x + x2 = 0 Move the constant term to the right: Add '21' to each side of the equation. -21 + -16x + 21 + x2 = 0 + 21 Reorder the terms: -21 + 21 + -16x + x2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -16x + x2 = 0 + 21 -16x + x2 = 0 + 21 Combine like terms: 0 + 21 = 21 -16x + x2 = 21 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 = 21 + 64 Reorder the terms: 64 + -16x + x2 = 21 + 64 Combine like terms: 21 + 64 = 85 64 + -16x + x2 = 85 Factor a perfect square on the left side: (x + -8)(x + -8) = 85 Calculate the square root of the right side: 9.219544457 Break this problem into two subproblems by setting (x + -8) equal to 9.219544457 and -9.219544457.Subproblem 1
x + -8 = 9.219544457 Simplifying x + -8 = 9.219544457 Reorder the terms: -8 + x = 9.219544457 Solving -8 + x = 9.219544457 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 = 9.219544457 + 8 Combine like terms: -8 + 8 = 0 0 + x = 9.219544457 + 8 x = 9.219544457 + 8 Combine like terms: 9.219544457 + 8 = 17.219544457 x = 17.219544457 Simplifying x = 17.219544457Subproblem 2
x + -8 = -9.219544457 Simplifying x + -8 = -9.219544457 Reorder the terms: -8 + x = -9.219544457 Solving -8 + x = -9.219544457 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 = -9.219544457 + 8 Combine like terms: -8 + 8 = 0 0 + x = -9.219544457 + 8 x = -9.219544457 + 8 Combine like terms: -9.219544457 + 8 = -1.219544457 x = -1.219544457 Simplifying x = -1.219544457Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.219544457, -1.219544457}
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