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Simplifying 2x2 + 36x + -15 = 0 Reorder the terms: -15 + 36x + 2x2 = 0 Solving -15 + 36x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -7.5 + 18x + x2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + 18x + 7.5 + x2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + 18x + x2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + 18x + x2 = 0 + 7.5 18x + x2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 18x + x2 = 7.5 The x term is 18x. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18x + 81 + x2 = 7.5 + 81 Reorder the terms: 81 + 18x + x2 = 7.5 + 81 Combine like terms: 7.5 + 81 = 88.5 81 + 18x + x2 = 88.5 Factor a perfect square on the left side: (x + 9)(x + 9) = 88.5 Calculate the square root of the right side: 9.407443861 Break this problem into two subproblems by setting (x + 9) equal to 9.407443861 and -9.407443861.Subproblem 1
x + 9 = 9.407443861 Simplifying x + 9 = 9.407443861 Reorder the terms: 9 + x = 9.407443861 Solving 9 + x = 9.407443861 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 9.407443861 + -9 Combine like terms: 9 + -9 = 0 0 + x = 9.407443861 + -9 x = 9.407443861 + -9 Combine like terms: 9.407443861 + -9 = 0.407443861 x = 0.407443861 Simplifying x = 0.407443861Subproblem 2
x + 9 = -9.407443861 Simplifying x + 9 = -9.407443861 Reorder the terms: 9 + x = -9.407443861 Solving 9 + x = -9.407443861 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = -9.407443861 + -9 Combine like terms: 9 + -9 = 0 0 + x = -9.407443861 + -9 x = -9.407443861 + -9 Combine like terms: -9.407443861 + -9 = -18.407443861 x = -18.407443861 Simplifying x = -18.407443861Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.407443861, -18.407443861}
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