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Simplifying 7x2 + -114x + -25 = 0 Reorder the terms: -25 + -114x + 7x2 = 0 Solving -25 + -114x + 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'. -3.571428571 + -16.28571429x + x2 = 0 Move the constant term to the right: Add '3.571428571' to each side of the equation. -3.571428571 + -16.28571429x + 3.571428571 + x2 = 0 + 3.571428571 Reorder the terms: -3.571428571 + 3.571428571 + -16.28571429x + x2 = 0 + 3.571428571 Combine like terms: -3.571428571 + 3.571428571 = 0.000000000 0.000000000 + -16.28571429x + x2 = 0 + 3.571428571 -16.28571429x + x2 = 0 + 3.571428571 Combine like terms: 0 + 3.571428571 = 3.571428571 -16.28571429x + x2 = 3.571428571 The x term is -16.28571429x. Take half its coefficient (-8.142857145). Square it (66.30612248) and add it to both sides. Add '66.30612248' to each side of the equation. -16.28571429x + 66.30612248 + x2 = 3.571428571 + 66.30612248 Reorder the terms: 66.30612248 + -16.28571429x + x2 = 3.571428571 + 66.30612248 Combine like terms: 3.571428571 + 66.30612248 = 69.877551051 66.30612248 + -16.28571429x + x2 = 69.877551051 Factor a perfect square on the left side: (x + -8.142857145)(x + -8.142857145) = 69.877551051 Calculate the square root of the right side: 8.359279338 Break this problem into two subproblems by setting (x + -8.142857145) equal to 8.359279338 and -8.359279338.Subproblem 1
x + -8.142857145 = 8.359279338 Simplifying x + -8.142857145 = 8.359279338 Reorder the terms: -8.142857145 + x = 8.359279338 Solving -8.142857145 + x = 8.359279338 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.142857145' to each side of the equation. -8.142857145 + 8.142857145 + x = 8.359279338 + 8.142857145 Combine like terms: -8.142857145 + 8.142857145 = 0.000000000 0.000000000 + x = 8.359279338 + 8.142857145 x = 8.359279338 + 8.142857145 Combine like terms: 8.359279338 + 8.142857145 = 16.502136483 x = 16.502136483 Simplifying x = 16.502136483Subproblem 2
x + -8.142857145 = -8.359279338 Simplifying x + -8.142857145 = -8.359279338 Reorder the terms: -8.142857145 + x = -8.359279338 Solving -8.142857145 + x = -8.359279338 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.142857145' to each side of the equation. -8.142857145 + 8.142857145 + x = -8.359279338 + 8.142857145 Combine like terms: -8.142857145 + 8.142857145 = 0.000000000 0.000000000 + x = -8.359279338 + 8.142857145 x = -8.359279338 + 8.142857145 Combine like terms: -8.359279338 + 8.142857145 = -0.216422193 x = -0.216422193 Simplifying x = -0.216422193Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.502136483, -0.216422193}
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