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Simplifying 5x2 + -27x + -90 = 0 Reorder the terms: -90 + -27x + 5x2 = 0 Solving -90 + -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'. -18 + -5.4x + x2 = 0 Move the constant term to the right: Add '18' to each side of the equation. -18 + -5.4x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + -5.4x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -5.4x + x2 = 0 + 18 -5.4x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 -5.4x + x2 = 18 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 = 18 + 7.29 Reorder the terms: 7.29 + -5.4x + x2 = 18 + 7.29 Combine like terms: 18 + 7.29 = 25.29 7.29 + -5.4x + x2 = 25.29 Factor a perfect square on the left side: (x + -2.7)(x + -2.7) = 25.29 Calculate the square root of the right side: 5.028916384 Break this problem into two subproblems by setting (x + -2.7) equal to 5.028916384 and -5.028916384.Subproblem 1
x + -2.7 = 5.028916384 Simplifying x + -2.7 = 5.028916384 Reorder the terms: -2.7 + x = 5.028916384 Solving -2.7 + x = 5.028916384 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 = 5.028916384 + 2.7 Combine like terms: -2.7 + 2.7 = 0.0 0.0 + x = 5.028916384 + 2.7 x = 5.028916384 + 2.7 Combine like terms: 5.028916384 + 2.7 = 7.728916384 x = 7.728916384 Simplifying x = 7.728916384Subproblem 2
x + -2.7 = -5.028916384 Simplifying x + -2.7 = -5.028916384 Reorder the terms: -2.7 + x = -5.028916384 Solving -2.7 + x = -5.028916384 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 = -5.028916384 + 2.7 Combine like terms: -2.7 + 2.7 = 0.0 0.0 + x = -5.028916384 + 2.7 x = -5.028916384 + 2.7 Combine like terms: -5.028916384 + 2.7 = -2.328916384 x = -2.328916384 Simplifying x = -2.328916384Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.728916384, -2.328916384}
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