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Simplifying 5x2 + -34x + 9 = 0 Reorder the terms: 9 + -34x + 5x2 = 0 Solving 9 + -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'. 1.8 + -6.8x + x2 = 0 Move the constant term to the right: Add '-1.8' to each side of the equation. 1.8 + -6.8x + -1.8 + x2 = 0 + -1.8 Reorder the terms: 1.8 + -1.8 + -6.8x + x2 = 0 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + -6.8x + x2 = 0 + -1.8 -6.8x + x2 = 0 + -1.8 Combine like terms: 0 + -1.8 = -1.8 -6.8x + x2 = -1.8 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 = -1.8 + 11.56 Reorder the terms: 11.56 + -6.8x + x2 = -1.8 + 11.56 Combine like terms: -1.8 + 11.56 = 9.76 11.56 + -6.8x + x2 = 9.76 Factor a perfect square on the left side: (x + -3.4)(x + -3.4) = 9.76 Calculate the square root of the right side: 3.12409987 Break this problem into two subproblems by setting (x + -3.4) equal to 3.12409987 and -3.12409987.Subproblem 1
x + -3.4 = 3.12409987 Simplifying x + -3.4 = 3.12409987 Reorder the terms: -3.4 + x = 3.12409987 Solving -3.4 + x = 3.12409987 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 = 3.12409987 + 3.4 Combine like terms: -3.4 + 3.4 = 0.0 0.0 + x = 3.12409987 + 3.4 x = 3.12409987 + 3.4 Combine like terms: 3.12409987 + 3.4 = 6.52409987 x = 6.52409987 Simplifying x = 6.52409987Subproblem 2
x + -3.4 = -3.12409987 Simplifying x + -3.4 = -3.12409987 Reorder the terms: -3.4 + x = -3.12409987 Solving -3.4 + x = -3.12409987 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 = -3.12409987 + 3.4 Combine like terms: -3.4 + 3.4 = 0.0 0.0 + x = -3.12409987 + 3.4 x = -3.12409987 + 3.4 Combine like terms: -3.12409987 + 3.4 = 0.27590013 x = 0.27590013 Simplifying x = 0.27590013Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.52409987, 0.27590013}
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