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Simplifying 12x2 + 36x + -53 = 0 Reorder the terms: -53 + 36x + 12x2 = 0 Solving -53 + 36x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -4.416666667 + 3x + x2 = 0 Move the constant term to the right: Add '4.416666667' to each side of the equation. -4.416666667 + 3x + 4.416666667 + x2 = 0 + 4.416666667 Reorder the terms: -4.416666667 + 4.416666667 + 3x + x2 = 0 + 4.416666667 Combine like terms: -4.416666667 + 4.416666667 = 0.000000000 0.000000000 + 3x + x2 = 0 + 4.416666667 3x + x2 = 0 + 4.416666667 Combine like terms: 0 + 4.416666667 = 4.416666667 3x + x2 = 4.416666667 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 = 4.416666667 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 4.416666667 + 2.25 Combine like terms: 4.416666667 + 2.25 = 6.666666667 2.25 + 3x + x2 = 6.666666667 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 6.666666667 Calculate the square root of the right side: 2.581988898 Break this problem into two subproblems by setting (x + 1.5) equal to 2.581988898 and -2.581988898.Subproblem 1
x + 1.5 = 2.581988898 Simplifying x + 1.5 = 2.581988898 Reorder the terms: 1.5 + x = 2.581988898 Solving 1.5 + x = 2.581988898 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 = 2.581988898 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 2.581988898 + -1.5 x = 2.581988898 + -1.5 Combine like terms: 2.581988898 + -1.5 = 1.081988898 x = 1.081988898 Simplifying x = 1.081988898Subproblem 2
x + 1.5 = -2.581988898 Simplifying x + 1.5 = -2.581988898 Reorder the terms: 1.5 + x = -2.581988898 Solving 1.5 + x = -2.581988898 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 = -2.581988898 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -2.581988898 + -1.5 x = -2.581988898 + -1.5 Combine like terms: -2.581988898 + -1.5 = -4.081988898 x = -4.081988898 Simplifying x = -4.081988898Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.081988898, -4.081988898}
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