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Simplifying 7x2 + 10x + -62 = 0 Reorder the terms: -62 + 10x + 7x2 = 0 Solving -62 + 10x + 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'. -8.857142857 + 1.428571429x + x2 = 0 Move the constant term to the right: Add '8.857142857' to each side of the equation. -8.857142857 + 1.428571429x + 8.857142857 + x2 = 0 + 8.857142857 Reorder the terms: -8.857142857 + 8.857142857 + 1.428571429x + x2 = 0 + 8.857142857 Combine like terms: -8.857142857 + 8.857142857 = 0.000000000 0.000000000 + 1.428571429x + x2 = 0 + 8.857142857 1.428571429x + x2 = 0 + 8.857142857 Combine like terms: 0 + 8.857142857 = 8.857142857 1.428571429x + x2 = 8.857142857 The x term is 1.428571429x. Take half its coefficient (0.7142857145). Square it (0.5102040819) and add it to both sides. Add '0.5102040819' to each side of the equation. 1.428571429x + 0.5102040819 + x2 = 8.857142857 + 0.5102040819 Reorder the terms: 0.5102040819 + 1.428571429x + x2 = 8.857142857 + 0.5102040819 Combine like terms: 8.857142857 + 0.5102040819 = 9.3673469389 0.5102040819 + 1.428571429x + x2 = 9.3673469389 Factor a perfect square on the left side: (x + 0.7142857145)(x + 0.7142857145) = 9.3673469389 Calculate the square root of the right side: 3.060612184 Break this problem into two subproblems by setting (x + 0.7142857145) equal to 3.060612184 and -3.060612184.Subproblem 1
x + 0.7142857145 = 3.060612184 Simplifying x + 0.7142857145 = 3.060612184 Reorder the terms: 0.7142857145 + x = 3.060612184 Solving 0.7142857145 + x = 3.060612184 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7142857145' to each side of the equation. 0.7142857145 + -0.7142857145 + x = 3.060612184 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + x = 3.060612184 + -0.7142857145 x = 3.060612184 + -0.7142857145 Combine like terms: 3.060612184 + -0.7142857145 = 2.3463264695 x = 2.3463264695 Simplifying x = 2.3463264695Subproblem 2
x + 0.7142857145 = -3.060612184 Simplifying x + 0.7142857145 = -3.060612184 Reorder the terms: 0.7142857145 + x = -3.060612184 Solving 0.7142857145 + x = -3.060612184 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7142857145' to each side of the equation. 0.7142857145 + -0.7142857145 + x = -3.060612184 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + x = -3.060612184 + -0.7142857145 x = -3.060612184 + -0.7142857145 Combine like terms: -3.060612184 + -0.7142857145 = -3.7748978985 x = -3.7748978985 Simplifying x = -3.7748978985Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.3463264695, -3.7748978985}
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