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Simplifying 10x2 + 5x + -18 = 0 Reorder the terms: -18 + 5x + 10x2 = 0 Solving -18 + 5x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.8 + 0.5x + x2 = 0 Move the constant term to the right: Add '1.8' to each side of the equation. -1.8 + 0.5x + 1.8 + x2 = 0 + 1.8 Reorder the terms: -1.8 + 1.8 + 0.5x + x2 = 0 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + 0.5x + x2 = 0 + 1.8 0.5x + x2 = 0 + 1.8 Combine like terms: 0 + 1.8 = 1.8 0.5x + x2 = 1.8 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 1.8 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 1.8 + 0.0625 Combine like terms: 1.8 + 0.0625 = 1.8625 0.0625 + 0.5x + x2 = 1.8625 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 1.8625 Calculate the square root of the right side: 1.364734406 Break this problem into two subproblems by setting (x + 0.25) equal to 1.364734406 and -1.364734406.Subproblem 1
x + 0.25 = 1.364734406 Simplifying x + 0.25 = 1.364734406 Reorder the terms: 0.25 + x = 1.364734406 Solving 0.25 + x = 1.364734406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 1.364734406 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 1.364734406 + -0.25 x = 1.364734406 + -0.25 Combine like terms: 1.364734406 + -0.25 = 1.114734406 x = 1.114734406 Simplifying x = 1.114734406Subproblem 2
x + 0.25 = -1.364734406 Simplifying x + 0.25 = -1.364734406 Reorder the terms: 0.25 + x = -1.364734406 Solving 0.25 + x = -1.364734406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -1.364734406 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -1.364734406 + -0.25 x = -1.364734406 + -0.25 Combine like terms: -1.364734406 + -0.25 = -1.614734406 x = -1.614734406 Simplifying x = -1.614734406Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.114734406, -1.614734406}
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