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Simplifying 0 = 5x2 + 7x + -245 Reorder the terms: 0 = -245 + 7x + 5x2 Solving 0 = -245 + 7x + 5x2 Solving for variable 'x'. Combine like terms: 0 + 245 = 245 245 + -7x + -5x2 = -245 + 7x + 5x2 + 245 + -7x + -5x2 Reorder the terms: 245 + -7x + -5x2 = -245 + 245 + 7x + -7x + 5x2 + -5x2 Combine like terms: -245 + 245 = 0 245 + -7x + -5x2 = 0 + 7x + -7x + 5x2 + -5x2 245 + -7x + -5x2 = 7x + -7x + 5x2 + -5x2 Combine like terms: 7x + -7x = 0 245 + -7x + -5x2 = 0 + 5x2 + -5x2 245 + -7x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 245 + -7x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -49 + 1.4x + x2 = 0 Move the constant term to the right: Add '49' to each side of the equation. -49 + 1.4x + 49 + x2 = 0 + 49 Reorder the terms: -49 + 49 + 1.4x + x2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + 1.4x + x2 = 0 + 49 1.4x + x2 = 0 + 49 Combine like terms: 0 + 49 = 49 1.4x + x2 = 49 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 = 49 + 0.49 Reorder the terms: 0.49 + 1.4x + x2 = 49 + 0.49 Combine like terms: 49 + 0.49 = 49.49 0.49 + 1.4x + x2 = 49.49 Factor a perfect square on the left side: (x + 0.7)(x + 0.7) = 49.49 Calculate the square root of the right side: 7.034912935 Break this problem into two subproblems by setting (x + 0.7) equal to 7.034912935 and -7.034912935.Subproblem 1
x + 0.7 = 7.034912935 Simplifying x + 0.7 = 7.034912935 Reorder the terms: 0.7 + x = 7.034912935 Solving 0.7 + x = 7.034912935 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 = 7.034912935 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = 7.034912935 + -0.7 x = 7.034912935 + -0.7 Combine like terms: 7.034912935 + -0.7 = 6.334912935 x = 6.334912935 Simplifying x = 6.334912935Subproblem 2
x + 0.7 = -7.034912935 Simplifying x + 0.7 = -7.034912935 Reorder the terms: 0.7 + x = -7.034912935 Solving 0.7 + x = -7.034912935 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 = -7.034912935 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = -7.034912935 + -0.7 x = -7.034912935 + -0.7 Combine like terms: -7.034912935 + -0.7 = -7.734912935 x = -7.734912935 Simplifying x = -7.734912935Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.334912935, -7.734912935}
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