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Simplifying 9x2 + 216x + 400 = 0 Reorder the terms: 400 + 216x + 9x2 = 0 Solving 400 + 216x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 44.44444444 + 24x + x2 = 0 Move the constant term to the right: Add '-44.44444444' to each side of the equation. 44.44444444 + 24x + -44.44444444 + x2 = 0 + -44.44444444 Reorder the terms: 44.44444444 + -44.44444444 + 24x + x2 = 0 + -44.44444444 Combine like terms: 44.44444444 + -44.44444444 = 0.00000000 0.00000000 + 24x + x2 = 0 + -44.44444444 24x + x2 = 0 + -44.44444444 Combine like terms: 0 + -44.44444444 = -44.44444444 24x + x2 = -44.44444444 The x term is 24x. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24x + 144 + x2 = -44.44444444 + 144 Reorder the terms: 144 + 24x + x2 = -44.44444444 + 144 Combine like terms: -44.44444444 + 144 = 99.55555556 144 + 24x + x2 = 99.55555556 Factor a perfect square on the left side: (x + 12)(x + 12) = 99.55555556 Calculate the square root of the right side: 9.977753032 Break this problem into two subproblems by setting (x + 12) equal to 9.977753032 and -9.977753032.Subproblem 1
x + 12 = 9.977753032 Simplifying x + 12 = 9.977753032 Reorder the terms: 12 + x = 9.977753032 Solving 12 + x = 9.977753032 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 9.977753032 + -12 Combine like terms: 12 + -12 = 0 0 + x = 9.977753032 + -12 x = 9.977753032 + -12 Combine like terms: 9.977753032 + -12 = -2.022246968 x = -2.022246968 Simplifying x = -2.022246968Subproblem 2
x + 12 = -9.977753032 Simplifying x + 12 = -9.977753032 Reorder the terms: 12 + x = -9.977753032 Solving 12 + x = -9.977753032 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = -9.977753032 + -12 Combine like terms: 12 + -12 = 0 0 + x = -9.977753032 + -12 x = -9.977753032 + -12 Combine like terms: -9.977753032 + -12 = -21.977753032 x = -21.977753032 Simplifying x = -21.977753032Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.022246968, -21.977753032}
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