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Simplifying 5x2 + 7x + -41 = 0 Reorder the terms: -41 + 7x + 5x2 = 0 Solving -41 + 7x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -8.2 + 1.4x + x2 = 0 Move the constant term to the right: Add '8.2' to each side of the equation. -8.2 + 1.4x + 8.2 + x2 = 0 + 8.2 Reorder the terms: -8.2 + 8.2 + 1.4x + x2 = 0 + 8.2 Combine like terms: -8.2 + 8.2 = 0.0 0.0 + 1.4x + x2 = 0 + 8.2 1.4x + x2 = 0 + 8.2 Combine like terms: 0 + 8.2 = 8.2 1.4x + x2 = 8.2 The x term is 1.4x. Take half its coefficient (0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. 1.4x + 0.49 + x2 = 8.2 + 0.49 Reorder the terms: 0.49 + 1.4x + x2 = 8.2 + 0.49 Combine like terms: 8.2 + 0.49 = 8.69 0.49 + 1.4x + x2 = 8.69 Factor a perfect square on the left side: (x + 0.7)(x + 0.7) = 8.69 Calculate the square root of the right side: 2.947880595 Break this problem into two subproblems by setting (x + 0.7) equal to 2.947880595 and -2.947880595.Subproblem 1
x + 0.7 = 2.947880595 Simplifying x + 0.7 = 2.947880595 Reorder the terms: 0.7 + x = 2.947880595 Solving 0.7 + x = 2.947880595 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + x = 2.947880595 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = 2.947880595 + -0.7 x = 2.947880595 + -0.7 Combine like terms: 2.947880595 + -0.7 = 2.247880595 x = 2.247880595 Simplifying x = 2.247880595Subproblem 2
x + 0.7 = -2.947880595 Simplifying x + 0.7 = -2.947880595 Reorder the terms: 0.7 + x = -2.947880595 Solving 0.7 + x = -2.947880595 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + x = -2.947880595 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = -2.947880595 + -0.7 x = -2.947880595 + -0.7 Combine like terms: -2.947880595 + -0.7 = -3.647880595 x = -3.647880595 Simplifying x = -3.647880595Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.247880595, -3.647880595}
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