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Simplifying 3x2 + -30x + 45 = 5 Reorder the terms: 45 + -30x + 3x2 = 5 Solving 45 + -30x + 3x2 = 5 Solving for variable 'x'. Reorder the terms: 45 + -5 + -30x + 3x2 = 5 + -5 Combine like terms: 45 + -5 = 40 40 + -30x + 3x2 = 5 + -5 Combine like terms: 5 + -5 = 0 40 + -30x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 13.33333333 + -10x + x2 = 0 Move the constant term to the right: Add '-13.33333333' to each side of the equation. 13.33333333 + -10x + -13.33333333 + x2 = 0 + -13.33333333 Reorder the terms: 13.33333333 + -13.33333333 + -10x + x2 = 0 + -13.33333333 Combine like terms: 13.33333333 + -13.33333333 = 0.00000000 0.00000000 + -10x + x2 = 0 + -13.33333333 -10x + x2 = 0 + -13.33333333 Combine like terms: 0 + -13.33333333 = -13.33333333 -10x + x2 = -13.33333333 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 = -13.33333333 + 25 Reorder the terms: 25 + -10x + x2 = -13.33333333 + 25 Combine like terms: -13.33333333 + 25 = 11.66666667 25 + -10x + x2 = 11.66666667 Factor a perfect square on the left side: (x + -5)(x + -5) = 11.66666667 Calculate the square root of the right side: 3.415650256 Break this problem into two subproblems by setting (x + -5) equal to 3.415650256 and -3.415650256.Subproblem 1
x + -5 = 3.415650256 Simplifying x + -5 = 3.415650256 Reorder the terms: -5 + x = 3.415650256 Solving -5 + x = 3.415650256 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 = 3.415650256 + 5 Combine like terms: -5 + 5 = 0 0 + x = 3.415650256 + 5 x = 3.415650256 + 5 Combine like terms: 3.415650256 + 5 = 8.415650256 x = 8.415650256 Simplifying x = 8.415650256Subproblem 2
x + -5 = -3.415650256 Simplifying x + -5 = -3.415650256 Reorder the terms: -5 + x = -3.415650256 Solving -5 + x = -3.415650256 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 = -3.415650256 + 5 Combine like terms: -5 + 5 = 0 0 + x = -3.415650256 + 5 x = -3.415650256 + 5 Combine like terms: -3.415650256 + 5 = 1.584349744 x = 1.584349744 Simplifying x = 1.584349744Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.415650256, 1.584349744}
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