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Simplifying 5x2 + 7x + -49 = 0 Reorder the terms: -49 + 7x + 5x2 = 0 Solving -49 + 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'. -9.8 + 1.4x + x2 = 0 Move the constant term to the right: Add '9.8' to each side of the equation. -9.8 + 1.4x + 9.8 + x2 = 0 + 9.8 Reorder the terms: -9.8 + 9.8 + 1.4x + x2 = 0 + 9.8 Combine like terms: -9.8 + 9.8 = 0.0 0.0 + 1.4x + x2 = 0 + 9.8 1.4x + x2 = 0 + 9.8 Combine like terms: 0 + 9.8 = 9.8 1.4x + x2 = 9.8 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 = 9.8 + 0.49 Reorder the terms: 0.49 + 1.4x + x2 = 9.8 + 0.49 Combine like terms: 9.8 + 0.49 = 10.29 0.49 + 1.4x + x2 = 10.29 Factor a perfect square on the left side: (x + 0.7)(x + 0.7) = 10.29 Calculate the square root of the right side: 3.207802986 Break this problem into two subproblems by setting (x + 0.7) equal to 3.207802986 and -3.207802986.Subproblem 1
x + 0.7 = 3.207802986 Simplifying x + 0.7 = 3.207802986 Reorder the terms: 0.7 + x = 3.207802986 Solving 0.7 + x = 3.207802986 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 = 3.207802986 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = 3.207802986 + -0.7 x = 3.207802986 + -0.7 Combine like terms: 3.207802986 + -0.7 = 2.507802986 x = 2.507802986 Simplifying x = 2.507802986Subproblem 2
x + 0.7 = -3.207802986 Simplifying x + 0.7 = -3.207802986 Reorder the terms: 0.7 + x = -3.207802986 Solving 0.7 + x = -3.207802986 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 = -3.207802986 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = -3.207802986 + -0.7 x = -3.207802986 + -0.7 Combine like terms: -3.207802986 + -0.7 = -3.907802986 x = -3.907802986 Simplifying x = -3.907802986Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.507802986, -3.907802986}
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