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Simplifying 7x2 + -1x + -49 = 0 Reorder the terms: -49 + -1x + 7x2 = 0 Solving -49 + -1x + 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'. -7 + -0.1428571429x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + -0.1428571429x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + -0.1428571429x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -0.1428571429x + x2 = 0 + 7 -0.1428571429x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 -0.1428571429x + x2 = 7 The x term is -0.1428571429x. Take half its coefficient (-0.07142857145). Square it (0.005102040819) and add it to both sides. Add '0.005102040819' to each side of the equation. -0.1428571429x + 0.005102040819 + x2 = 7 + 0.005102040819 Reorder the terms: 0.005102040819 + -0.1428571429x + x2 = 7 + 0.005102040819 Combine like terms: 7 + 0.005102040819 = 7.005102040819 0.005102040819 + -0.1428571429x + x2 = 7.005102040819 Factor a perfect square on the left side: (x + -0.07142857145)(x + -0.07142857145) = 7.005102040819 Calculate the square root of the right side: 2.646715331 Break this problem into two subproblems by setting (x + -0.07142857145) equal to 2.646715331 and -2.646715331.Subproblem 1
x + -0.07142857145 = 2.646715331 Simplifying x + -0.07142857145 = 2.646715331 Reorder the terms: -0.07142857145 + x = 2.646715331 Solving -0.07142857145 + x = 2.646715331 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.07142857145' to each side of the equation. -0.07142857145 + 0.07142857145 + x = 2.646715331 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + x = 2.646715331 + 0.07142857145 x = 2.646715331 + 0.07142857145 Combine like terms: 2.646715331 + 0.07142857145 = 2.71814390245 x = 2.71814390245 Simplifying x = 2.71814390245Subproblem 2
x + -0.07142857145 = -2.646715331 Simplifying x + -0.07142857145 = -2.646715331 Reorder the terms: -0.07142857145 + x = -2.646715331 Solving -0.07142857145 + x = -2.646715331 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.07142857145' to each side of the equation. -0.07142857145 + 0.07142857145 + x = -2.646715331 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + x = -2.646715331 + 0.07142857145 x = -2.646715331 + 0.07142857145 Combine like terms: -2.646715331 + 0.07142857145 = -2.57528675955 x = -2.57528675955 Simplifying x = -2.57528675955Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.71814390245, -2.57528675955}
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