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Simplifying 5x2 + -15x + -18 = 0 Reorder the terms: -18 + -15x + 5x2 = 0 Solving -18 + -15x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3.6 + -3x + x2 = 0 Move the constant term to the right: Add '3.6' to each side of the equation. -3.6 + -3x + 3.6 + x2 = 0 + 3.6 Reorder the terms: -3.6 + 3.6 + -3x + x2 = 0 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + -3x + x2 = 0 + 3.6 -3x + x2 = 0 + 3.6 Combine like terms: 0 + 3.6 = 3.6 -3x + x2 = 3.6 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 3.6 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 3.6 + 2.25 Combine like terms: 3.6 + 2.25 = 5.85 2.25 + -3x + x2 = 5.85 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 5.85 Calculate the square root of the right side: 2.418677324 Break this problem into two subproblems by setting (x + -1.5) equal to 2.418677324 and -2.418677324.Subproblem 1
x + -1.5 = 2.418677324 Simplifying x + -1.5 = 2.418677324 Reorder the terms: -1.5 + x = 2.418677324 Solving -1.5 + x = 2.418677324 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 2.418677324 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 2.418677324 + 1.5 x = 2.418677324 + 1.5 Combine like terms: 2.418677324 + 1.5 = 3.918677324 x = 3.918677324 Simplifying x = 3.918677324Subproblem 2
x + -1.5 = -2.418677324 Simplifying x + -1.5 = -2.418677324 Reorder the terms: -1.5 + x = -2.418677324 Solving -1.5 + x = -2.418677324 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -2.418677324 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -2.418677324 + 1.5 x = -2.418677324 + 1.5 Combine like terms: -2.418677324 + 1.5 = -0.918677324 x = -0.918677324 Simplifying x = -0.918677324Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.918677324, -0.918677324}
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