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Simplifying 5x2 + 14x + -81 = 0 Reorder the terms: -81 + 14x + 5x2 = 0 Solving -81 + 14x + 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'. -16.2 + 2.8x + x2 = 0 Move the constant term to the right: Add '16.2' to each side of the equation. -16.2 + 2.8x + 16.2 + x2 = 0 + 16.2 Reorder the terms: -16.2 + 16.2 + 2.8x + x2 = 0 + 16.2 Combine like terms: -16.2 + 16.2 = 0.0 0.0 + 2.8x + x2 = 0 + 16.2 2.8x + x2 = 0 + 16.2 Combine like terms: 0 + 16.2 = 16.2 2.8x + x2 = 16.2 The x term is 2.8x. Take half its coefficient (1.4). Square it (1.96) and add it to both sides. Add '1.96' to each side of the equation. 2.8x + 1.96 + x2 = 16.2 + 1.96 Reorder the terms: 1.96 + 2.8x + x2 = 16.2 + 1.96 Combine like terms: 16.2 + 1.96 = 18.16 1.96 + 2.8x + x2 = 18.16 Factor a perfect square on the left side: (x + 1.4)(x + 1.4) = 18.16 Calculate the square root of the right side: 4.261455151 Break this problem into two subproblems by setting (x + 1.4) equal to 4.261455151 and -4.261455151.Subproblem 1
x + 1.4 = 4.261455151 Simplifying x + 1.4 = 4.261455151 Reorder the terms: 1.4 + x = 4.261455151 Solving 1.4 + x = 4.261455151 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.4' to each side of the equation. 1.4 + -1.4 + x = 4.261455151 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + x = 4.261455151 + -1.4 x = 4.261455151 + -1.4 Combine like terms: 4.261455151 + -1.4 = 2.861455151 x = 2.861455151 Simplifying x = 2.861455151Subproblem 2
x + 1.4 = -4.261455151 Simplifying x + 1.4 = -4.261455151 Reorder the terms: 1.4 + x = -4.261455151 Solving 1.4 + x = -4.261455151 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.4' to each side of the equation. 1.4 + -1.4 + x = -4.261455151 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + x = -4.261455151 + -1.4 x = -4.261455151 + -1.4 Combine like terms: -4.261455151 + -1.4 = -5.661455151 x = -5.661455151 Simplifying x = -5.661455151Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.861455151, -5.661455151}
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