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Simplifying 4123x2 + 643x + -532 = 0 Reorder the terms: -532 + 643x + 4123x2 = 0 Solving -532 + 643x + 4123x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4123 the coefficient of the squared term: Divide each side by '4123'. -0.1290322581 + 0.1559544021x + x2 = 0 Move the constant term to the right: Add '0.1290322581' to each side of the equation. -0.1290322581 + 0.1559544021x + 0.1290322581 + x2 = 0 + 0.1290322581 Reorder the terms: -0.1290322581 + 0.1290322581 + 0.1559544021x + x2 = 0 + 0.1290322581 Combine like terms: -0.1290322581 + 0.1290322581 = 0.0000000000 0.0000000000 + 0.1559544021x + x2 = 0 + 0.1290322581 0.1559544021x + x2 = 0 + 0.1290322581 Combine like terms: 0 + 0.1290322581 = 0.1290322581 0.1559544021x + x2 = 0.1290322581 The x term is 0.1559544021x. Take half its coefficient (0.07797720105). Square it (0.006080443884) and add it to both sides. Add '0.006080443884' to each side of the equation. 0.1559544021x + 0.006080443884 + x2 = 0.1290322581 + 0.006080443884 Reorder the terms: 0.006080443884 + 0.1559544021x + x2 = 0.1290322581 + 0.006080443884 Combine like terms: 0.1290322581 + 0.006080443884 = 0.135112701984 0.006080443884 + 0.1559544021x + x2 = 0.135112701984 Factor a perfect square on the left side: (x + 0.07797720105)(x + 0.07797720105) = 0.135112701984 Calculate the square root of the right side: 0.367576797 Break this problem into two subproblems by setting (x + 0.07797720105) equal to 0.367576797 and -0.367576797.Subproblem 1
x + 0.07797720105 = 0.367576797 Simplifying x + 0.07797720105 = 0.367576797 Reorder the terms: 0.07797720105 + x = 0.367576797 Solving 0.07797720105 + x = 0.367576797 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.07797720105' to each side of the equation. 0.07797720105 + -0.07797720105 + x = 0.367576797 + -0.07797720105 Combine like terms: 0.07797720105 + -0.07797720105 = 0.00000000000 0.00000000000 + x = 0.367576797 + -0.07797720105 x = 0.367576797 + -0.07797720105 Combine like terms: 0.367576797 + -0.07797720105 = 0.28959959595 x = 0.28959959595 Simplifying x = 0.28959959595Subproblem 2
x + 0.07797720105 = -0.367576797 Simplifying x + 0.07797720105 = -0.367576797 Reorder the terms: 0.07797720105 + x = -0.367576797 Solving 0.07797720105 + x = -0.367576797 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.07797720105' to each side of the equation. 0.07797720105 + -0.07797720105 + x = -0.367576797 + -0.07797720105 Combine like terms: 0.07797720105 + -0.07797720105 = 0.00000000000 0.00000000000 + x = -0.367576797 + -0.07797720105 x = -0.367576797 + -0.07797720105 Combine like terms: -0.367576797 + -0.07797720105 = -0.44555399805 x = -0.44555399805 Simplifying x = -0.44555399805Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.28959959595, -0.44555399805}
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