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Simplifying 9x2 + 45x + -14 = 0 Reorder the terms: -14 + 45x + 9x2 = 0 Solving -14 + 45x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.555555556 + 5x + x2 = 0 Move the constant term to the right: Add '1.555555556' to each side of the equation. -1.555555556 + 5x + 1.555555556 + x2 = 0 + 1.555555556 Reorder the terms: -1.555555556 + 1.555555556 + 5x + x2 = 0 + 1.555555556 Combine like terms: -1.555555556 + 1.555555556 = 0.000000000 0.000000000 + 5x + x2 = 0 + 1.555555556 5x + x2 = 0 + 1.555555556 Combine like terms: 0 + 1.555555556 = 1.555555556 5x + x2 = 1.555555556 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 1.555555556 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 1.555555556 + 6.25 Combine like terms: 1.555555556 + 6.25 = 7.805555556 6.25 + 5x + x2 = 7.805555556 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 7.805555556 Calculate the square root of the right side: 2.793842436 Break this problem into two subproblems by setting (x + 2.5) equal to 2.793842436 and -2.793842436.Subproblem 1
x + 2.5 = 2.793842436 Simplifying x + 2.5 = 2.793842436 Reorder the terms: 2.5 + x = 2.793842436 Solving 2.5 + x = 2.793842436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 2.793842436 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 2.793842436 + -2.5 x = 2.793842436 + -2.5 Combine like terms: 2.793842436 + -2.5 = 0.293842436 x = 0.293842436 Simplifying x = 0.293842436Subproblem 2
x + 2.5 = -2.793842436 Simplifying x + 2.5 = -2.793842436 Reorder the terms: 2.5 + x = -2.793842436 Solving 2.5 + x = -2.793842436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -2.793842436 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -2.793842436 + -2.5 x = -2.793842436 + -2.5 Combine like terms: -2.793842436 + -2.5 = -5.293842436 x = -5.293842436 Simplifying x = -5.293842436Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.293842436, -5.293842436}
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