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Simplifying 5x2 + -90x + 229 = 0 Reorder the terms: 229 + -90x + 5x2 = 0 Solving 229 + -90x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 45.8 + -18x + x2 = 0 Move the constant term to the right: Add '-45.8' to each side of the equation. 45.8 + -18x + -45.8 + x2 = 0 + -45.8 Reorder the terms: 45.8 + -45.8 + -18x + x2 = 0 + -45.8 Combine like terms: 45.8 + -45.8 = 0.0 0.0 + -18x + x2 = 0 + -45.8 -18x + x2 = 0 + -45.8 Combine like terms: 0 + -45.8 = -45.8 -18x + x2 = -45.8 The x term is -18x. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x + 81 + x2 = -45.8 + 81 Reorder the terms: 81 + -18x + x2 = -45.8 + 81 Combine like terms: -45.8 + 81 = 35.2 81 + -18x + x2 = 35.2 Factor a perfect square on the left side: (x + -9)(x + -9) = 35.2 Calculate the square root of the right side: 5.93295879 Break this problem into two subproblems by setting (x + -9) equal to 5.93295879 and -5.93295879.Subproblem 1
x + -9 = 5.93295879 Simplifying x + -9 = 5.93295879 Reorder the terms: -9 + x = 5.93295879 Solving -9 + x = 5.93295879 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 5.93295879 + 9 Combine like terms: -9 + 9 = 0 0 + x = 5.93295879 + 9 x = 5.93295879 + 9 Combine like terms: 5.93295879 + 9 = 14.93295879 x = 14.93295879 Simplifying x = 14.93295879Subproblem 2
x + -9 = -5.93295879 Simplifying x + -9 = -5.93295879 Reorder the terms: -9 + x = -5.93295879 Solving -9 + x = -5.93295879 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -5.93295879 + 9 Combine like terms: -9 + 9 = 0 0 + x = -5.93295879 + 9 x = -5.93295879 + 9 Combine like terms: -5.93295879 + 9 = 3.06704121 x = 3.06704121 Simplifying x = 3.06704121Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.93295879, 3.06704121}
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