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Simplifying x(5x + -18) = 180 Reorder the terms: x(-18 + 5x) = 180 (-18 * x + 5x * x) = 180 (-18x + 5x2) = 180 Solving -18x + 5x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + -18x + 5x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + -18x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -36 + -3.6x + x2 = 0 Move the constant term to the right: Add '36' to each side of the equation. -36 + -3.6x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + -3.6x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -3.6x + x2 = 0 + 36 -3.6x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 -3.6x + x2 = 36 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 = 36 + 3.24 Reorder the terms: 3.24 + -3.6x + x2 = 36 + 3.24 Combine like terms: 36 + 3.24 = 39.24 3.24 + -3.6x + x2 = 39.24 Factor a perfect square on the left side: (x + -1.8)(x + -1.8) = 39.24 Calculate the square root of the right side: 6.264183905 Break this problem into two subproblems by setting (x + -1.8) equal to 6.264183905 and -6.264183905.Subproblem 1
x + -1.8 = 6.264183905 Simplifying x + -1.8 = 6.264183905 Reorder the terms: -1.8 + x = 6.264183905 Solving -1.8 + x = 6.264183905 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 = 6.264183905 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = 6.264183905 + 1.8 x = 6.264183905 + 1.8 Combine like terms: 6.264183905 + 1.8 = 8.064183905 x = 8.064183905 Simplifying x = 8.064183905Subproblem 2
x + -1.8 = -6.264183905 Simplifying x + -1.8 = -6.264183905 Reorder the terms: -1.8 + x = -6.264183905 Solving -1.8 + x = -6.264183905 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 = -6.264183905 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = -6.264183905 + 1.8 x = -6.264183905 + 1.8 Combine like terms: -6.264183905 + 1.8 = -4.464183905 x = -4.464183905 Simplifying x = -4.464183905Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.064183905, -4.464183905}
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