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Simplifying 0 = 10X2 + 30X + -9 Reorder the terms: 0 = -9 + 30X + 10X2 Solving 0 = -9 + 30X + 10X2 Solving for variable 'X'. Combine like terms: 0 + 9 = 9 9 + -30X + -10X2 = -9 + 30X + 10X2 + 9 + -30X + -10X2 Reorder the terms: 9 + -30X + -10X2 = -9 + 9 + 30X + -30X + 10X2 + -10X2 Combine like terms: -9 + 9 = 0 9 + -30X + -10X2 = 0 + 30X + -30X + 10X2 + -10X2 9 + -30X + -10X2 = 30X + -30X + 10X2 + -10X2 Combine like terms: 30X + -30X = 0 9 + -30X + -10X2 = 0 + 10X2 + -10X2 9 + -30X + -10X2 = 10X2 + -10X2 Combine like terms: 10X2 + -10X2 = 0 9 + -30X + -10X2 = 0 Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -0.9 + 3X + X2 = 0 Move the constant term to the right: Add '0.9' to each side of the equation. -0.9 + 3X + 0.9 + X2 = 0 + 0.9 Reorder the terms: -0.9 + 0.9 + 3X + X2 = 0 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + 3X + X2 = 0 + 0.9 3X + X2 = 0 + 0.9 Combine like terms: 0 + 0.9 = 0.9 3X + X2 = 0.9 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 = 0.9 + 2.25 Reorder the terms: 2.25 + 3X + X2 = 0.9 + 2.25 Combine like terms: 0.9 + 2.25 = 3.15 2.25 + 3X + X2 = 3.15 Factor a perfect square on the left side: (X + 1.5)(X + 1.5) = 3.15 Calculate the square root of the right side: 1.774823935 Break this problem into two subproblems by setting (X + 1.5) equal to 1.774823935 and -1.774823935.Subproblem 1
X + 1.5 = 1.774823935 Simplifying X + 1.5 = 1.774823935 Reorder the terms: 1.5 + X = 1.774823935 Solving 1.5 + X = 1.774823935 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 = 1.774823935 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + X = 1.774823935 + -1.5 X = 1.774823935 + -1.5 Combine like terms: 1.774823935 + -1.5 = 0.274823935 X = 0.274823935 Simplifying X = 0.274823935Subproblem 2
X + 1.5 = -1.774823935 Simplifying X + 1.5 = -1.774823935 Reorder the terms: 1.5 + X = -1.774823935 Solving 1.5 + X = -1.774823935 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 = -1.774823935 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + X = -1.774823935 + -1.5 X = -1.774823935 + -1.5 Combine like terms: -1.774823935 + -1.5 = -3.274823935 X = -3.274823935 Simplifying X = -3.274823935Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.274823935, -3.274823935}
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