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Simplifying 5x2 + -40x + 9 = 0 Reorder the terms: 9 + -40x + 5x2 = 0 Solving 9 + -40x + 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'. 1.8 + -8x + x2 = 0 Move the constant term to the right: Add '-1.8' to each side of the equation. 1.8 + -8x + -1.8 + x2 = 0 + -1.8 Reorder the terms: 1.8 + -1.8 + -8x + x2 = 0 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + -8x + x2 = 0 + -1.8 -8x + x2 = 0 + -1.8 Combine like terms: 0 + -1.8 = -1.8 -8x + x2 = -1.8 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -1.8 + 16 Reorder the terms: 16 + -8x + x2 = -1.8 + 16 Combine like terms: -1.8 + 16 = 14.2 16 + -8x + x2 = 14.2 Factor a perfect square on the left side: (x + -4)(x + -4) = 14.2 Calculate the square root of the right side: 3.768288736 Break this problem into two subproblems by setting (x + -4) equal to 3.768288736 and -3.768288736.Subproblem 1
x + -4 = 3.768288736 Simplifying x + -4 = 3.768288736 Reorder the terms: -4 + x = 3.768288736 Solving -4 + x = 3.768288736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 3.768288736 + 4 Combine like terms: -4 + 4 = 0 0 + x = 3.768288736 + 4 x = 3.768288736 + 4 Combine like terms: 3.768288736 + 4 = 7.768288736 x = 7.768288736 Simplifying x = 7.768288736Subproblem 2
x + -4 = -3.768288736 Simplifying x + -4 = -3.768288736 Reorder the terms: -4 + x = -3.768288736 Solving -4 + x = -3.768288736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -3.768288736 + 4 Combine like terms: -4 + 4 = 0 0 + x = -3.768288736 + 4 x = -3.768288736 + 4 Combine like terms: -3.768288736 + 4 = 0.231711264 x = 0.231711264 Simplifying x = 0.231711264Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.768288736, 0.231711264}
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