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Simplifying 9x2 + 63x + 4 = 0 Reorder the terms: 4 + 63x + 9x2 = 0 Solving 4 + 63x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.4444444444 + 7x + x2 = 0 Move the constant term to the right: Add '-0.4444444444' to each side of the equation. 0.4444444444 + 7x + -0.4444444444 + x2 = 0 + -0.4444444444 Reorder the terms: 0.4444444444 + -0.4444444444 + 7x + x2 = 0 + -0.4444444444 Combine like terms: 0.4444444444 + -0.4444444444 = 0.0000000000 0.0000000000 + 7x + x2 = 0 + -0.4444444444 7x + x2 = 0 + -0.4444444444 Combine like terms: 0 + -0.4444444444 = -0.4444444444 7x + x2 = -0.4444444444 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = -0.4444444444 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -0.4444444444 + 12.25 Combine like terms: -0.4444444444 + 12.25 = 11.8055555556 12.25 + 7x + x2 = 11.8055555556 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 11.8055555556 Calculate the square root of the right side: 3.435921355 Break this problem into two subproblems by setting (x + 3.5) equal to 3.435921355 and -3.435921355.Subproblem 1
x + 3.5 = 3.435921355 Simplifying x + 3.5 = 3.435921355 Reorder the terms: 3.5 + x = 3.435921355 Solving 3.5 + x = 3.435921355 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 3.435921355 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 3.435921355 + -3.5 x = 3.435921355 + -3.5 Combine like terms: 3.435921355 + -3.5 = -0.064078645 x = -0.064078645 Simplifying x = -0.064078645Subproblem 2
x + 3.5 = -3.435921355 Simplifying x + 3.5 = -3.435921355 Reorder the terms: 3.5 + x = -3.435921355 Solving 3.5 + x = -3.435921355 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -3.435921355 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -3.435921355 + -3.5 x = -3.435921355 + -3.5 Combine like terms: -3.435921355 + -3.5 = -6.935921355 x = -6.935921355 Simplifying x = -6.935921355Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.064078645, -6.935921355}
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