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Simplifying 9x2 + 90x + 223 = 0 Reorder the terms: 223 + 90x + 9x2 = 0 Solving 223 + 90x + 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'. 24.77777778 + 10x + x2 = 0 Move the constant term to the right: Add '-24.77777778' to each side of the equation. 24.77777778 + 10x + -24.77777778 + x2 = 0 + -24.77777778 Reorder the terms: 24.77777778 + -24.77777778 + 10x + x2 = 0 + -24.77777778 Combine like terms: 24.77777778 + -24.77777778 = 0.00000000 0.00000000 + 10x + x2 = 0 + -24.77777778 10x + x2 = 0 + -24.77777778 Combine like terms: 0 + -24.77777778 = -24.77777778 10x + x2 = -24.77777778 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = -24.77777778 + 25 Reorder the terms: 25 + 10x + x2 = -24.77777778 + 25 Combine like terms: -24.77777778 + 25 = 0.22222222 25 + 10x + x2 = 0.22222222 Factor a perfect square on the left side: (x + 5)(x + 5) = 0.22222222 Calculate the square root of the right side: 0.471404518 Break this problem into two subproblems by setting (x + 5) equal to 0.471404518 and -0.471404518.Subproblem 1
x + 5 = 0.471404518 Simplifying x + 5 = 0.471404518 Reorder the terms: 5 + x = 0.471404518 Solving 5 + x = 0.471404518 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 0.471404518 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0.471404518 + -5 x = 0.471404518 + -5 Combine like terms: 0.471404518 + -5 = -4.528595482 x = -4.528595482 Simplifying x = -4.528595482Subproblem 2
x + 5 = -0.471404518 Simplifying x + 5 = -0.471404518 Reorder the terms: 5 + x = -0.471404518 Solving 5 + x = -0.471404518 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -0.471404518 + -5 Combine like terms: 5 + -5 = 0 0 + x = -0.471404518 + -5 x = -0.471404518 + -5 Combine like terms: -0.471404518 + -5 = -5.471404518 x = -5.471404518 Simplifying x = -5.471404518Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.528595482, -5.471404518}
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