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Simplifying 3x2 + 30x = 65 Reorder the terms: 30x + 3x2 = 65 Solving 30x + 3x2 = 65 Solving for variable 'x'. Reorder the terms: -65 + 30x + 3x2 = 65 + -65 Combine like terms: 65 + -65 = 0 -65 + 30x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -21.66666667 + 10x + x2 = 0 Move the constant term to the right: Add '21.66666667' to each side of the equation. -21.66666667 + 10x + 21.66666667 + x2 = 0 + 21.66666667 Reorder the terms: -21.66666667 + 21.66666667 + 10x + x2 = 0 + 21.66666667 Combine like terms: -21.66666667 + 21.66666667 = 0.00000000 0.00000000 + 10x + x2 = 0 + 21.66666667 10x + x2 = 0 + 21.66666667 Combine like terms: 0 + 21.66666667 = 21.66666667 10x + x2 = 21.66666667 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 = 21.66666667 + 25 Reorder the terms: 25 + 10x + x2 = 21.66666667 + 25 Combine like terms: 21.66666667 + 25 = 46.66666667 25 + 10x + x2 = 46.66666667 Factor a perfect square on the left side: (x + 5)(x + 5) = 46.66666667 Calculate the square root of the right side: 6.831300511 Break this problem into two subproblems by setting (x + 5) equal to 6.831300511 and -6.831300511.Subproblem 1
x + 5 = 6.831300511 Simplifying x + 5 = 6.831300511 Reorder the terms: 5 + x = 6.831300511 Solving 5 + x = 6.831300511 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 = 6.831300511 + -5 Combine like terms: 5 + -5 = 0 0 + x = 6.831300511 + -5 x = 6.831300511 + -5 Combine like terms: 6.831300511 + -5 = 1.831300511 x = 1.831300511 Simplifying x = 1.831300511Subproblem 2
x + 5 = -6.831300511 Simplifying x + 5 = -6.831300511 Reorder the terms: 5 + x = -6.831300511 Solving 5 + x = -6.831300511 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 = -6.831300511 + -5 Combine like terms: 5 + -5 = 0 0 + x = -6.831300511 + -5 x = -6.831300511 + -5 Combine like terms: -6.831300511 + -5 = -11.831300511 x = -11.831300511 Simplifying x = -11.831300511Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.831300511, -11.831300511}
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