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Simplifying 0 = x2 + 17x + -21 Reorder the terms: 0 = -21 + 17x + x2 Solving 0 = -21 + 17x + x2 Solving for variable 'x'. Combine like terms: 0 + 21 = 21 21 + -17x + -1x2 = -21 + 17x + x2 + 21 + -17x + -1x2 Reorder the terms: 21 + -17x + -1x2 = -21 + 21 + 17x + -17x + x2 + -1x2 Combine like terms: -21 + 21 = 0 21 + -17x + -1x2 = 0 + 17x + -17x + x2 + -1x2 21 + -17x + -1x2 = 17x + -17x + x2 + -1x2 Combine like terms: 17x + -17x = 0 21 + -17x + -1x2 = 0 + x2 + -1x2 21 + -17x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 21 + -17x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -21 + 17x + x2 = 0 Move the constant term to the right: Add '21' to each side of the equation. -21 + 17x + 21 + x2 = 0 + 21 Reorder the terms: -21 + 21 + 17x + x2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 17x + x2 = 0 + 21 17x + x2 = 0 + 21 Combine like terms: 0 + 21 = 21 17x + x2 = 21 The x term is 17x. Take half its coefficient (8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. 17x + 72.25 + x2 = 21 + 72.25 Reorder the terms: 72.25 + 17x + x2 = 21 + 72.25 Combine like terms: 21 + 72.25 = 93.25 72.25 + 17x + x2 = 93.25 Factor a perfect square on the left side: (x + 8.5)(x + 8.5) = 93.25 Calculate the square root of the right side: 9.656603958 Break this problem into two subproblems by setting (x + 8.5) equal to 9.656603958 and -9.656603958.Subproblem 1
x + 8.5 = 9.656603958 Simplifying x + 8.5 = 9.656603958 Reorder the terms: 8.5 + x = 9.656603958 Solving 8.5 + x = 9.656603958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = 9.656603958 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = 9.656603958 + -8.5 x = 9.656603958 + -8.5 Combine like terms: 9.656603958 + -8.5 = 1.156603958 x = 1.156603958 Simplifying x = 1.156603958Subproblem 2
x + 8.5 = -9.656603958 Simplifying x + 8.5 = -9.656603958 Reorder the terms: 8.5 + x = -9.656603958 Solving 8.5 + x = -9.656603958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = -9.656603958 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = -9.656603958 + -8.5 x = -9.656603958 + -8.5 Combine like terms: -9.656603958 + -8.5 = -18.156603958 x = -18.156603958 Simplifying x = -18.156603958Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.156603958, -18.156603958}
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