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Simplifying 36x + 10x2 = 14 Solving 36x + 10x2 = 14 Solving for variable 'x'. Reorder the terms: -14 + 36x + 10x2 = 14 + -14 Combine like terms: 14 + -14 = 0 -14 + 36x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + 18x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + 18x + 5x2)' equal to zero and attempt to solve: Simplifying -7 + 18x + 5x2 = 0 Solving -7 + 18x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.4 + 3.6x + x2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + 3.6x + 1.4 + x2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + 3.6x + x2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + 3.6x + x2 = 0 + 1.4 3.6x + x2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 3.6x + x2 = 1.4 The x term is 3.6x. Take half its coefficient (1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. 3.6x + 3.24 + x2 = 1.4 + 3.24 Reorder the terms: 3.24 + 3.6x + x2 = 1.4 + 3.24 Combine like terms: 1.4 + 3.24 = 4.64 3.24 + 3.6x + x2 = 4.64 Factor a perfect square on the left side: (x + 1.8)(x + 1.8) = 4.64 Calculate the square root of the right side: 2.154065923 Break this problem into two subproblems by setting (x + 1.8) equal to 2.154065923 and -2.154065923.Subproblem 1
x + 1.8 = 2.154065923 Simplifying x + 1.8 = 2.154065923 Reorder the terms: 1.8 + x = 2.154065923 Solving 1.8 + x = 2.154065923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + x = 2.154065923 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + x = 2.154065923 + -1.8 x = 2.154065923 + -1.8 Combine like terms: 2.154065923 + -1.8 = 0.354065923 x = 0.354065923 Simplifying x = 0.354065923Subproblem 2
x + 1.8 = -2.154065923 Simplifying x + 1.8 = -2.154065923 Reorder the terms: 1.8 + x = -2.154065923 Solving 1.8 + x = -2.154065923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + x = -2.154065923 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + x = -2.154065923 + -1.8 x = -2.154065923 + -1.8 Combine like terms: -2.154065923 + -1.8 = -3.954065923 x = -3.954065923 Simplifying x = -3.954065923Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.354065923, -3.954065923}Solution
x = {0.354065923, -3.954065923}
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