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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 = 5.471404518 x = 5.471404518 Simplifying x = 5.471404518Subproblem 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 = 4.528595482 x = 4.528595482 Simplifying x = 4.528595482Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.471404518, 4.528595482}
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