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Simplifying 9x2 + 14x + 3 = 0 Reorder the terms: 3 + 14x + 9x2 = 0 Solving 3 + 14x + 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'. 0.3333333333 + 1.555555556x + x2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + 1.555555556x + -0.3333333333 + x2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + 1.555555556x + x2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + 1.555555556x + x2 = 0 + -0.3333333333 1.555555556x + x2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 1.555555556x + x2 = -0.3333333333 The x term is 1.555555556x. Take half its coefficient (0.777777778). Square it (0.6049382720) and add it to both sides. Add '0.6049382720' to each side of the equation. 1.555555556x + 0.6049382720 + x2 = -0.3333333333 + 0.6049382720 Reorder the terms: 0.6049382720 + 1.555555556x + x2 = -0.3333333333 + 0.6049382720 Combine like terms: -0.3333333333 + 0.6049382720 = 0.2716049387 0.6049382720 + 1.555555556x + x2 = 0.2716049387 Factor a perfect square on the left side: (x + 0.777777778)(x + 0.777777778) = 0.2716049387 Calculate the square root of the right side: 0.521157307 Break this problem into two subproblems by setting (x + 0.777777778) equal to 0.521157307 and -0.521157307.Subproblem 1
x + 0.777777778 = 0.521157307 Simplifying x + 0.777777778 = 0.521157307 Reorder the terms: 0.777777778 + x = 0.521157307 Solving 0.777777778 + x = 0.521157307 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.777777778' to each side of the equation. 0.777777778 + -0.777777778 + x = 0.521157307 + -0.777777778 Combine like terms: 0.777777778 + -0.777777778 = 0.000000000 0.000000000 + x = 0.521157307 + -0.777777778 x = 0.521157307 + -0.777777778 Combine like terms: 0.521157307 + -0.777777778 = -0.256620471 x = -0.256620471 Simplifying x = -0.256620471Subproblem 2
x + 0.777777778 = -0.521157307 Simplifying x + 0.777777778 = -0.521157307 Reorder the terms: 0.777777778 + x = -0.521157307 Solving 0.777777778 + x = -0.521157307 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.777777778' to each side of the equation. 0.777777778 + -0.777777778 + x = -0.521157307 + -0.777777778 Combine like terms: 0.777777778 + -0.777777778 = 0.000000000 0.000000000 + x = -0.521157307 + -0.777777778 x = -0.521157307 + -0.777777778 Combine like terms: -0.521157307 + -0.777777778 = -1.298935085 x = -1.298935085 Simplifying x = -1.298935085Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.256620471, -1.298935085}
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