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Simplifying x2 + -21x + 69 = 0 Reorder the terms: 69 + -21x + x2 = 0 Solving 69 + -21x + 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 + -21x + -69 + x2 = 0 + -69 Reorder the terms: 69 + -69 + -21x + x2 = 0 + -69 Combine like terms: 69 + -69 = 0 0 + -21x + x2 = 0 + -69 -21x + x2 = 0 + -69 Combine like terms: 0 + -69 = -69 -21x + x2 = -69 The x term is -21x. Take half its coefficient (-10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. -21x + 110.25 + x2 = -69 + 110.25 Reorder the terms: 110.25 + -21x + x2 = -69 + 110.25 Combine like terms: -69 + 110.25 = 41.25 110.25 + -21x + x2 = 41.25 Factor a perfect square on the left side: (x + -10.5)(x + -10.5) = 41.25 Calculate the square root of the right side: 6.422616289 Break this problem into two subproblems by setting (x + -10.5) equal to 6.422616289 and -6.422616289.Subproblem 1
x + -10.5 = 6.422616289 Simplifying x + -10.5 = 6.422616289 Reorder the terms: -10.5 + x = 6.422616289 Solving -10.5 + x = 6.422616289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = 6.422616289 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = 6.422616289 + 10.5 x = 6.422616289 + 10.5 Combine like terms: 6.422616289 + 10.5 = 16.922616289 x = 16.922616289 Simplifying x = 16.922616289Subproblem 2
x + -10.5 = -6.422616289 Simplifying x + -10.5 = -6.422616289 Reorder the terms: -10.5 + x = -6.422616289 Solving -10.5 + x = -6.422616289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = -6.422616289 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = -6.422616289 + 10.5 x = -6.422616289 + 10.5 Combine like terms: -6.422616289 + 10.5 = 4.077383711 x = 4.077383711 Simplifying x = 4.077383711Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.922616289, 4.077383711}
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