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Simplifying 3x2 + -30x + 2 = 0 Reorder the terms: 2 + -30x + 3x2 = 0 Solving 2 + -30x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.6666666667 + -10x + x2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + -10x + -0.6666666667 + x2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + -10x + x2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + -10x + x2 = 0 + -0.6666666667 -10x + x2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 -10x + x2 = -0.6666666667 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 = -0.6666666667 + 25 Reorder the terms: 25 + -10x + x2 = -0.6666666667 + 25 Combine like terms: -0.6666666667 + 25 = 24.3333333333 25 + -10x + x2 = 24.3333333333 Factor a perfect square on the left side: (x + -5)(x + -5) = 24.3333333333 Calculate the square root of the right side: 4.932882862 Break this problem into two subproblems by setting (x + -5) equal to 4.932882862 and -4.932882862.Subproblem 1
x + -5 = 4.932882862 Simplifying x + -5 = 4.932882862 Reorder the terms: -5 + x = 4.932882862 Solving -5 + x = 4.932882862 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 = 4.932882862 + 5 Combine like terms: -5 + 5 = 0 0 + x = 4.932882862 + 5 x = 4.932882862 + 5 Combine like terms: 4.932882862 + 5 = 9.932882862 x = 9.932882862 Simplifying x = 9.932882862Subproblem 2
x + -5 = -4.932882862 Simplifying x + -5 = -4.932882862 Reorder the terms: -5 + x = -4.932882862 Solving -5 + x = -4.932882862 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 = -4.932882862 + 5 Combine like terms: -5 + 5 = 0 0 + x = -4.932882862 + 5 x = -4.932882862 + 5 Combine like terms: -4.932882862 + 5 = 0.067117138 x = 0.067117138 Simplifying x = 0.067117138Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.932882862, 0.067117138}
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