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Simplifying x(5x + -18) + 90 = 180 Reorder the terms: x(-18 + 5x) + 90 = 180 (-18 * x + 5x * x) + 90 = 180 (-18x + 5x2) + 90 = 180 Reorder the terms: 90 + -18x + 5x2 = 180 Solving 90 + -18x + 5x2 = 180 Solving for variable 'x'. Reorder the terms: 90 + -180 + -18x + 5x2 = 180 + -180 Combine like terms: 90 + -180 = -90 -90 + -18x + 5x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -90 + -18x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -18 + -3.6x + x2 = 0 Move the constant term to the right: Add '18' to each side of the equation. -18 + -3.6x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + -3.6x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -3.6x + x2 = 0 + 18 -3.6x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 -3.6x + x2 = 18 The x term is -3.6x. Take half its coefficient (-1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. -3.6x + 3.24 + x2 = 18 + 3.24 Reorder the terms: 3.24 + -3.6x + x2 = 18 + 3.24 Combine like terms: 18 + 3.24 = 21.24 3.24 + -3.6x + x2 = 21.24 Factor a perfect square on the left side: (x + -1.8)(x + -1.8) = 21.24 Calculate the square root of the right side: 4.608687449 Break this problem into two subproblems by setting (x + -1.8) equal to 4.608687449 and -4.608687449.Subproblem 1
x + -1.8 = 4.608687449 Simplifying x + -1.8 = 4.608687449 Reorder the terms: -1.8 + x = 4.608687449 Solving -1.8 + x = 4.608687449 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + x = 4.608687449 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = 4.608687449 + 1.8 x = 4.608687449 + 1.8 Combine like terms: 4.608687449 + 1.8 = 6.408687449 x = 6.408687449 Simplifying x = 6.408687449Subproblem 2
x + -1.8 = -4.608687449 Simplifying x + -1.8 = -4.608687449 Reorder the terms: -1.8 + x = -4.608687449 Solving -1.8 + x = -4.608687449 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + x = -4.608687449 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = -4.608687449 + 1.8 x = -4.608687449 + 1.8 Combine like terms: -4.608687449 + 1.8 = -2.808687449 x = -2.808687449 Simplifying x = -2.808687449Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.408687449, -2.808687449}
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