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Simplifying x2 + 5x * 6 = 180 Reorder the terms for easier multiplication: x2 + 5 * 6x = 180 Multiply 5 * 6 x2 + 30x = 180 Reorder the terms: 30x + x2 = 180 Solving 30x + x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + 30x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + 30x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '180' to each side of the equation. -180 + 30x + 180 + x2 = 0 + 180 Reorder the terms: -180 + 180 + 30x + x2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + 30x + x2 = 0 + 180 30x + x2 = 0 + 180 Combine like terms: 0 + 180 = 180 30x + x2 = 180 The x term is 30x. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30x + 225 + x2 = 180 + 225 Reorder the terms: 225 + 30x + x2 = 180 + 225 Combine like terms: 180 + 225 = 405 225 + 30x + x2 = 405 Factor a perfect square on the left side: (x + 15)(x + 15) = 405 Calculate the square root of the right side: 20.124611797 Break this problem into two subproblems by setting (x + 15) equal to 20.124611797 and -20.124611797.Subproblem 1
x + 15 = 20.124611797 Simplifying x + 15 = 20.124611797 Reorder the terms: 15 + x = 20.124611797 Solving 15 + x = 20.124611797 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 20.124611797 + -15 Combine like terms: 15 + -15 = 0 0 + x = 20.124611797 + -15 x = 20.124611797 + -15 Combine like terms: 20.124611797 + -15 = 5.124611797 x = 5.124611797 Simplifying x = 5.124611797Subproblem 2
x + 15 = -20.124611797 Simplifying x + 15 = -20.124611797 Reorder the terms: 15 + x = -20.124611797 Solving 15 + x = -20.124611797 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = -20.124611797 + -15 Combine like terms: 15 + -15 = 0 0 + x = -20.124611797 + -15 x = -20.124611797 + -15 Combine like terms: -20.124611797 + -15 = -35.124611797 x = -35.124611797 Simplifying x = -35.124611797Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.124611797, -35.124611797}
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