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Simplifying 5.32x2 + 3.31x + -1.35 = 0 Reorder the terms: -1.35 + 3.31x + 5.32x2 = 0 Solving -1.35 + 3.31x + 5.32x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5.32 the coefficient of the squared term: Divide each side by '5.32'. -0.2537593985 + 0.6221804511x + x2 = 0 Move the constant term to the right: Add '0.2537593985' to each side of the equation. -0.2537593985 + 0.6221804511x + 0.2537593985 + x2 = 0 + 0.2537593985 Reorder the terms: -0.2537593985 + 0.2537593985 + 0.6221804511x + x2 = 0 + 0.2537593985 Combine like terms: -0.2537593985 + 0.2537593985 = 0.0000000000 0.0000000000 + 0.6221804511x + x2 = 0 + 0.2537593985 0.6221804511x + x2 = 0 + 0.2537593985 Combine like terms: 0 + 0.2537593985 = 0.2537593985 0.6221804511x + x2 = 0.2537593985 The x term is 0.6221804511x. Take half its coefficient (0.3110902256). Square it (0.09677712846) and add it to both sides. Add '0.09677712846' to each side of the equation. 0.6221804511x + 0.09677712846 + x2 = 0.2537593985 + 0.09677712846 Reorder the terms: 0.09677712846 + 0.6221804511x + x2 = 0.2537593985 + 0.09677712846 Combine like terms: 0.2537593985 + 0.09677712846 = 0.35053652696 0.09677712846 + 0.6221804511x + x2 = 0.35053652696 Factor a perfect square on the left side: (x + 0.3110902256)(x + 0.3110902256) = 0.35053652696 Calculate the square root of the right side: 0.592061253 Break this problem into two subproblems by setting (x + 0.3110902256) equal to 0.592061253 and -0.592061253.Subproblem 1
x + 0.3110902256 = 0.592061253 Simplifying x + 0.3110902256 = 0.592061253 Reorder the terms: 0.3110902256 + x = 0.592061253 Solving 0.3110902256 + x = 0.592061253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3110902256' to each side of the equation. 0.3110902256 + -0.3110902256 + x = 0.592061253 + -0.3110902256 Combine like terms: 0.3110902256 + -0.3110902256 = 0.0000000000 0.0000000000 + x = 0.592061253 + -0.3110902256 x = 0.592061253 + -0.3110902256 Combine like terms: 0.592061253 + -0.3110902256 = 0.2809710274 x = 0.2809710274 Simplifying x = 0.2809710274Subproblem 2
x + 0.3110902256 = -0.592061253 Simplifying x + 0.3110902256 = -0.592061253 Reorder the terms: 0.3110902256 + x = -0.592061253 Solving 0.3110902256 + x = -0.592061253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3110902256' to each side of the equation. 0.3110902256 + -0.3110902256 + x = -0.592061253 + -0.3110902256 Combine like terms: 0.3110902256 + -0.3110902256 = 0.0000000000 0.0000000000 + x = -0.592061253 + -0.3110902256 x = -0.592061253 + -0.3110902256 Combine like terms: -0.592061253 + -0.3110902256 = -0.9031514786 x = -0.9031514786 Simplifying x = -0.9031514786Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2809710274, -0.9031514786}
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