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Simplifying 0 = 122 + 7x + -5x(x) Multiply x * x 0 = 122 + 7x + -5x2 Solving 0 = 122 + 7x + -5x2 Solving for variable 'x'. Combine like terms: 0 + -122 = -122 -122 + -7x + 5x2 = 122 + 7x + -5x2 + -122 + -7x + 5x2 Reorder the terms: -122 + -7x + 5x2 = 122 + -122 + 7x + -7x + -5x2 + 5x2 Combine like terms: 122 + -122 = 0 -122 + -7x + 5x2 = 0 + 7x + -7x + -5x2 + 5x2 -122 + -7x + 5x2 = 7x + -7x + -5x2 + 5x2 Combine like terms: 7x + -7x = 0 -122 + -7x + 5x2 = 0 + -5x2 + 5x2 -122 + -7x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 -122 + -7x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -24.4 + -1.4x + x2 = 0 Move the constant term to the right: Add '24.4' to each side of the equation. -24.4 + -1.4x + 24.4 + x2 = 0 + 24.4 Reorder the terms: -24.4 + 24.4 + -1.4x + x2 = 0 + 24.4 Combine like terms: -24.4 + 24.4 = 0.0 0.0 + -1.4x + x2 = 0 + 24.4 -1.4x + x2 = 0 + 24.4 Combine like terms: 0 + 24.4 = 24.4 -1.4x + x2 = 24.4 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 = 24.4 + 0.49 Reorder the terms: 0.49 + -1.4x + x2 = 24.4 + 0.49 Combine like terms: 24.4 + 0.49 = 24.89 0.49 + -1.4x + x2 = 24.89 Factor a perfect square on the left side: (x + -0.7)(x + -0.7) = 24.89 Calculate the square root of the right side: 4.988987873 Break this problem into two subproblems by setting (x + -0.7) equal to 4.988987873 and -4.988987873.Subproblem 1
x + -0.7 = 4.988987873 Simplifying x + -0.7 = 4.988987873 Reorder the terms: -0.7 + x = 4.988987873 Solving -0.7 + x = 4.988987873 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 = 4.988987873 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = 4.988987873 + 0.7 x = 4.988987873 + 0.7 Combine like terms: 4.988987873 + 0.7 = 5.688987873 x = 5.688987873 Simplifying x = 5.688987873Subproblem 2
x + -0.7 = -4.988987873 Simplifying x + -0.7 = -4.988987873 Reorder the terms: -0.7 + x = -4.988987873 Solving -0.7 + x = -4.988987873 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 = -4.988987873 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = -4.988987873 + 0.7 x = -4.988987873 + 0.7 Combine like terms: -4.988987873 + 0.7 = -4.288987873 x = -4.288987873 Simplifying x = -4.288987873Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.688987873, -4.288987873}
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