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Simplifying 5x2 + 27x + -98 = 0 Reorder the terms: -98 + 27x + 5x2 = 0 Solving -98 + 27x + 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'. -19.6 + 5.4x + x2 = 0 Move the constant term to the right: Add '19.6' to each side of the equation. -19.6 + 5.4x + 19.6 + x2 = 0 + 19.6 Reorder the terms: -19.6 + 19.6 + 5.4x + x2 = 0 + 19.6 Combine like terms: -19.6 + 19.6 = 0.0 0.0 + 5.4x + x2 = 0 + 19.6 5.4x + x2 = 0 + 19.6 Combine like terms: 0 + 19.6 = 19.6 5.4x + x2 = 19.6 The x term is 5.4x. Take half its coefficient (2.7). Square it (7.29) and add it to both sides. Add '7.29' to each side of the equation. 5.4x + 7.29 + x2 = 19.6 + 7.29 Reorder the terms: 7.29 + 5.4x + x2 = 19.6 + 7.29 Combine like terms: 19.6 + 7.29 = 26.89 7.29 + 5.4x + x2 = 26.89 Factor a perfect square on the left side: (x + 2.7)(x + 2.7) = 26.89 Calculate the square root of the right side: 5.185556865 Break this problem into two subproblems by setting (x + 2.7) equal to 5.185556865 and -5.185556865.Subproblem 1
x + 2.7 = 5.185556865 Simplifying x + 2.7 = 5.185556865 Reorder the terms: 2.7 + x = 5.185556865 Solving 2.7 + x = 5.185556865 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.7' to each side of the equation. 2.7 + -2.7 + x = 5.185556865 + -2.7 Combine like terms: 2.7 + -2.7 = 0.0 0.0 + x = 5.185556865 + -2.7 x = 5.185556865 + -2.7 Combine like terms: 5.185556865 + -2.7 = 2.485556865 x = 2.485556865 Simplifying x = 2.485556865Subproblem 2
x + 2.7 = -5.185556865 Simplifying x + 2.7 = -5.185556865 Reorder the terms: 2.7 + x = -5.185556865 Solving 2.7 + x = -5.185556865 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.7' to each side of the equation. 2.7 + -2.7 + x = -5.185556865 + -2.7 Combine like terms: 2.7 + -2.7 = 0.0 0.0 + x = -5.185556865 + -2.7 x = -5.185556865 + -2.7 Combine like terms: -5.185556865 + -2.7 = -7.885556865 x = -7.885556865 Simplifying x = -7.885556865Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.485556865, -7.885556865}
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