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Simplifying 62x2 + -108x + -27 = 0 Reorder the terms: -27 + -108x + 62x2 = 0 Solving -27 + -108x + 62x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 62 the coefficient of the squared term: Divide each side by '62'. -0.435483871 + -1.741935484x + x2 = 0 Move the constant term to the right: Add '0.435483871' to each side of the equation. -0.435483871 + -1.741935484x + 0.435483871 + x2 = 0 + 0.435483871 Reorder the terms: -0.435483871 + 0.435483871 + -1.741935484x + x2 = 0 + 0.435483871 Combine like terms: -0.435483871 + 0.435483871 = 0.000000000 0.000000000 + -1.741935484x + x2 = 0 + 0.435483871 -1.741935484x + x2 = 0 + 0.435483871 Combine like terms: 0 + 0.435483871 = 0.435483871 -1.741935484x + x2 = 0.435483871 The x term is -1.741935484x. Take half its coefficient (-0.870967742). Square it (0.7585848076) and add it to both sides. Add '0.7585848076' to each side of the equation. -1.741935484x + 0.7585848076 + x2 = 0.435483871 + 0.7585848076 Reorder the terms: 0.7585848076 + -1.741935484x + x2 = 0.435483871 + 0.7585848076 Combine like terms: 0.435483871 + 0.7585848076 = 1.1940686786 0.7585848076 + -1.741935484x + x2 = 1.1940686786 Factor a perfect square on the left side: (x + -0.870967742)(x + -0.870967742) = 1.1940686786 Calculate the square root of the right side: 1.092734496 Break this problem into two subproblems by setting (x + -0.870967742) equal to 1.092734496 and -1.092734496.Subproblem 1
x + -0.870967742 = 1.092734496 Simplifying x + -0.870967742 = 1.092734496 Reorder the terms: -0.870967742 + x = 1.092734496 Solving -0.870967742 + x = 1.092734496 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.870967742' to each side of the equation. -0.870967742 + 0.870967742 + x = 1.092734496 + 0.870967742 Combine like terms: -0.870967742 + 0.870967742 = 0.000000000 0.000000000 + x = 1.092734496 + 0.870967742 x = 1.092734496 + 0.870967742 Combine like terms: 1.092734496 + 0.870967742 = 1.963702238 x = 1.963702238 Simplifying x = 1.963702238Subproblem 2
x + -0.870967742 = -1.092734496 Simplifying x + -0.870967742 = -1.092734496 Reorder the terms: -0.870967742 + x = -1.092734496 Solving -0.870967742 + x = -1.092734496 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.870967742' to each side of the equation. -0.870967742 + 0.870967742 + x = -1.092734496 + 0.870967742 Combine like terms: -0.870967742 + 0.870967742 = 0.000000000 0.000000000 + x = -1.092734496 + 0.870967742 x = -1.092734496 + 0.870967742 Combine like terms: -1.092734496 + 0.870967742 = -0.221766754 x = -0.221766754 Simplifying x = -0.221766754Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.963702238, -0.221766754}
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