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Simplifying 7x2 + -42x + 9 = 0 Reorder the terms: 9 + -42x + 7x2 = 0 Solving 9 + -42x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 1.285714286 + -6x + x2 = 0 Move the constant term to the right: Add '-1.285714286' to each side of the equation. 1.285714286 + -6x + -1.285714286 + x2 = 0 + -1.285714286 Reorder the terms: 1.285714286 + -1.285714286 + -6x + x2 = 0 + -1.285714286 Combine like terms: 1.285714286 + -1.285714286 = 0.000000000 0.000000000 + -6x + x2 = 0 + -1.285714286 -6x + x2 = 0 + -1.285714286 Combine like terms: 0 + -1.285714286 = -1.285714286 -6x + x2 = -1.285714286 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -1.285714286 + 9 Reorder the terms: 9 + -6x + x2 = -1.285714286 + 9 Combine like terms: -1.285714286 + 9 = 7.714285714 9 + -6x + x2 = 7.714285714 Factor a perfect square on the left side: (x + -3)(x + -3) = 7.714285714 Calculate the square root of the right side: 2.777460299 Break this problem into two subproblems by setting (x + -3) equal to 2.777460299 and -2.777460299.Subproblem 1
x + -3 = 2.777460299 Simplifying x + -3 = 2.777460299 Reorder the terms: -3 + x = 2.777460299 Solving -3 + x = 2.777460299 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 2.777460299 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.777460299 + 3 x = 2.777460299 + 3 Combine like terms: 2.777460299 + 3 = 5.777460299 x = 5.777460299 Simplifying x = 5.777460299Subproblem 2
x + -3 = -2.777460299 Simplifying x + -3 = -2.777460299 Reorder the terms: -3 + x = -2.777460299 Solving -3 + x = -2.777460299 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -2.777460299 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.777460299 + 3 x = -2.777460299 + 3 Combine like terms: -2.777460299 + 3 = 0.222539701 x = 0.222539701 Simplifying x = 0.222539701Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.777460299, 0.222539701}
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