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Simplifying 7x2 + 5x + -174 = 0 Reorder the terms: -174 + 5x + 7x2 = 0 Solving -174 + 5x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -24.85714286 + 0.7142857143x + x2 = 0 Move the constant term to the right: Add '24.85714286' to each side of the equation. -24.85714286 + 0.7142857143x + 24.85714286 + x2 = 0 + 24.85714286 Reorder the terms: -24.85714286 + 24.85714286 + 0.7142857143x + x2 = 0 + 24.85714286 Combine like terms: -24.85714286 + 24.85714286 = 0.00000000 0.00000000 + 0.7142857143x + x2 = 0 + 24.85714286 0.7142857143x + x2 = 0 + 24.85714286 Combine like terms: 0 + 24.85714286 = 24.85714286 0.7142857143x + x2 = 24.85714286 The x term is 0.7142857143x. Take half its coefficient (0.3571428572). Square it (0.1275510204) and add it to both sides. Add '0.1275510204' to each side of the equation. 0.7142857143x + 0.1275510204 + x2 = 24.85714286 + 0.1275510204 Reorder the terms: 0.1275510204 + 0.7142857143x + x2 = 24.85714286 + 0.1275510204 Combine like terms: 24.85714286 + 0.1275510204 = 24.9846938804 0.1275510204 + 0.7142857143x + x2 = 24.9846938804 Factor a perfect square on the left side: (x + 0.3571428572)(x + 0.3571428572) = 24.9846938804 Calculate the square root of the right side: 4.998469154 Break this problem into two subproblems by setting (x + 0.3571428572) equal to 4.998469154 and -4.998469154.Subproblem 1
x + 0.3571428572 = 4.998469154 Simplifying x + 0.3571428572 = 4.998469154 Reorder the terms: 0.3571428572 + x = 4.998469154 Solving 0.3571428572 + x = 4.998469154 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3571428572' to each side of the equation. 0.3571428572 + -0.3571428572 + x = 4.998469154 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + x = 4.998469154 + -0.3571428572 x = 4.998469154 + -0.3571428572 Combine like terms: 4.998469154 + -0.3571428572 = 4.6413262968 x = 4.6413262968 Simplifying x = 4.6413262968Subproblem 2
x + 0.3571428572 = -4.998469154 Simplifying x + 0.3571428572 = -4.998469154 Reorder the terms: 0.3571428572 + x = -4.998469154 Solving 0.3571428572 + x = -4.998469154 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3571428572' to each side of the equation. 0.3571428572 + -0.3571428572 + x = -4.998469154 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + x = -4.998469154 + -0.3571428572 x = -4.998469154 + -0.3571428572 Combine like terms: -4.998469154 + -0.3571428572 = -5.3556120112 x = -5.3556120112 Simplifying x = -5.3556120112Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.6413262968, -5.3556120112}
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