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Simplifying x2 + 17x + 69 = 0 Reorder the terms: 69 + 17x + x2 = 0 Solving 69 + 17x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-69' to each side of the equation. 69 + 17x + -69 + x2 = 0 + -69 Reorder the terms: 69 + -69 + 17x + x2 = 0 + -69 Combine like terms: 69 + -69 = 0 0 + 17x + x2 = 0 + -69 17x + x2 = 0 + -69 Combine like terms: 0 + -69 = -69 17x + x2 = -69 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 = -69 + 72.25 Reorder the terms: 72.25 + 17x + x2 = -69 + 72.25 Combine like terms: -69 + 72.25 = 3.25 72.25 + 17x + x2 = 3.25 Factor a perfect square on the left side: (x + 8.5)(x + 8.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (x + 8.5) equal to 1.802775638 and -1.802775638.Subproblem 1
x + 8.5 = 1.802775638 Simplifying x + 8.5 = 1.802775638 Reorder the terms: 8.5 + x = 1.802775638 Solving 8.5 + x = 1.802775638 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 = 1.802775638 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = 1.802775638 + -8.5 x = 1.802775638 + -8.5 Combine like terms: 1.802775638 + -8.5 = -6.697224362 x = -6.697224362 Simplifying x = -6.697224362Subproblem 2
x + 8.5 = -1.802775638 Simplifying x + 8.5 = -1.802775638 Reorder the terms: 8.5 + x = -1.802775638 Solving 8.5 + x = -1.802775638 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 = -1.802775638 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = -1.802775638 + -8.5 x = -1.802775638 + -8.5 Combine like terms: -1.802775638 + -8.5 = -10.302775638 x = -10.302775638 Simplifying x = -10.302775638Solution
The solution to the problem is based on the solutions from the subproblems. x = {-6.697224362, -10.302775638}
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