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Simplifying 5x2 + 34x + 34 = 0 Reorder the terms: 34 + 34x + 5x2 = 0 Solving 34 + 34x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 6.8 + 6.8x + x2 = 0 Move the constant term to the right: Add '-6.8' to each side of the equation. 6.8 + 6.8x + -6.8 + x2 = 0 + -6.8 Reorder the terms: 6.8 + -6.8 + 6.8x + x2 = 0 + -6.8 Combine like terms: 6.8 + -6.8 = 0.0 0.0 + 6.8x + x2 = 0 + -6.8 6.8x + x2 = 0 + -6.8 Combine like terms: 0 + -6.8 = -6.8 6.8x + x2 = -6.8 The x term is 6.8x. Take half its coefficient (3.4). Square it (11.56) and add it to both sides. Add '11.56' to each side of the equation. 6.8x + 11.56 + x2 = -6.8 + 11.56 Reorder the terms: 11.56 + 6.8x + x2 = -6.8 + 11.56 Combine like terms: -6.8 + 11.56 = 4.76 11.56 + 6.8x + x2 = 4.76 Factor a perfect square on the left side: (x + 3.4)(x + 3.4) = 4.76 Calculate the square root of the right side: 2.181742423 Break this problem into two subproblems by setting (x + 3.4) equal to 2.181742423 and -2.181742423.Subproblem 1
x + 3.4 = 2.181742423 Simplifying x + 3.4 = 2.181742423 Reorder the terms: 3.4 + x = 2.181742423 Solving 3.4 + x = 2.181742423 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.4' to each side of the equation. 3.4 + -3.4 + x = 2.181742423 + -3.4 Combine like terms: 3.4 + -3.4 = 0.0 0.0 + x = 2.181742423 + -3.4 x = 2.181742423 + -3.4 Combine like terms: 2.181742423 + -3.4 = -1.218257577 x = -1.218257577 Simplifying x = -1.218257577Subproblem 2
x + 3.4 = -2.181742423 Simplifying x + 3.4 = -2.181742423 Reorder the terms: 3.4 + x = -2.181742423 Solving 3.4 + x = -2.181742423 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.4' to each side of the equation. 3.4 + -3.4 + x = -2.181742423 + -3.4 Combine like terms: 3.4 + -3.4 = 0.0 0.0 + x = -2.181742423 + -3.4 x = -2.181742423 + -3.4 Combine like terms: -2.181742423 + -3.4 = -5.581742423 x = -5.581742423 Simplifying x = -5.581742423Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.218257577, -5.581742423}
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