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Simplifying 62x2 + 49x + -164 = 0 Reorder the terms: -164 + 49x + 62x2 = 0 Solving -164 + 49x + 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'. -2.64516129 + 0.7903225806x + x2 = 0 Move the constant term to the right: Add '2.64516129' to each side of the equation. -2.64516129 + 0.7903225806x + 2.64516129 + x2 = 0 + 2.64516129 Reorder the terms: -2.64516129 + 2.64516129 + 0.7903225806x + x2 = 0 + 2.64516129 Combine like terms: -2.64516129 + 2.64516129 = 0.00000000 0.00000000 + 0.7903225806x + x2 = 0 + 2.64516129 0.7903225806x + x2 = 0 + 2.64516129 Combine like terms: 0 + 2.64516129 = 2.64516129 0.7903225806x + x2 = 2.64516129 The x term is 0.7903225806x. Take half its coefficient (0.3951612903). Square it (0.1561524454) and add it to both sides. Add '0.1561524454' to each side of the equation. 0.7903225806x + 0.1561524454 + x2 = 2.64516129 + 0.1561524454 Reorder the terms: 0.1561524454 + 0.7903225806x + x2 = 2.64516129 + 0.1561524454 Combine like terms: 2.64516129 + 0.1561524454 = 2.8013137354 0.1561524454 + 0.7903225806x + x2 = 2.8013137354 Factor a perfect square on the left side: (x + 0.3951612903)(x + 0.3951612903) = 2.8013137354 Calculate the square root of the right side: 1.673712561 Break this problem into two subproblems by setting (x + 0.3951612903) equal to 1.673712561 and -1.673712561.Subproblem 1
x + 0.3951612903 = 1.673712561 Simplifying x + 0.3951612903 = 1.673712561 Reorder the terms: 0.3951612903 + x = 1.673712561 Solving 0.3951612903 + x = 1.673712561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3951612903' to each side of the equation. 0.3951612903 + -0.3951612903 + x = 1.673712561 + -0.3951612903 Combine like terms: 0.3951612903 + -0.3951612903 = 0.0000000000 0.0000000000 + x = 1.673712561 + -0.3951612903 x = 1.673712561 + -0.3951612903 Combine like terms: 1.673712561 + -0.3951612903 = 1.2785512707 x = 1.2785512707 Simplifying x = 1.2785512707Subproblem 2
x + 0.3951612903 = -1.673712561 Simplifying x + 0.3951612903 = -1.673712561 Reorder the terms: 0.3951612903 + x = -1.673712561 Solving 0.3951612903 + x = -1.673712561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3951612903' to each side of the equation. 0.3951612903 + -0.3951612903 + x = -1.673712561 + -0.3951612903 Combine like terms: 0.3951612903 + -0.3951612903 = 0.0000000000 0.0000000000 + x = -1.673712561 + -0.3951612903 x = -1.673712561 + -0.3951612903 Combine like terms: -1.673712561 + -0.3951612903 = -2.0688738513 x = -2.0688738513 Simplifying x = -2.0688738513Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2785512707, -2.0688738513}
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