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Simplifying 5x(x + 12) + 6 = 3 Reorder the terms: 5x(12 + x) + 6 = 3 (12 * 5x + x * 5x) + 6 = 3 (60x + 5x2) + 6 = 3 Reorder the terms: 6 + 60x + 5x2 = 3 Solving 6 + 60x + 5x2 = 3 Solving for variable 'x'. Reorder the terms: 6 + -3 + 60x + 5x2 = 3 + -3 Combine like terms: 6 + -3 = 3 3 + 60x + 5x2 = 3 + -3 Combine like terms: 3 + -3 = 0 3 + 60x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.6 + 12x + x2 = 0 Move the constant term to the right: Add '-0.6' to each side of the equation. 0.6 + 12x + -0.6 + x2 = 0 + -0.6 Reorder the terms: 0.6 + -0.6 + 12x + x2 = 0 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + 12x + x2 = 0 + -0.6 12x + x2 = 0 + -0.6 Combine like terms: 0 + -0.6 = -0.6 12x + x2 = -0.6 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = -0.6 + 36 Reorder the terms: 36 + 12x + x2 = -0.6 + 36 Combine like terms: -0.6 + 36 = 35.4 36 + 12x + x2 = 35.4 Factor a perfect square on the left side: (x + 6)(x + 6) = 35.4 Calculate the square root of the right side: 5.949789912 Break this problem into two subproblems by setting (x + 6) equal to 5.949789912 and -5.949789912.Subproblem 1
x + 6 = 5.949789912 Simplifying x + 6 = 5.949789912 Reorder the terms: 6 + x = 5.949789912 Solving 6 + x = 5.949789912 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 5.949789912 + -6 Combine like terms: 6 + -6 = 0 0 + x = 5.949789912 + -6 x = 5.949789912 + -6 Combine like terms: 5.949789912 + -6 = -0.050210088 x = -0.050210088 Simplifying x = -0.050210088Subproblem 2
x + 6 = -5.949789912 Simplifying x + 6 = -5.949789912 Reorder the terms: 6 + x = -5.949789912 Solving 6 + x = -5.949789912 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -5.949789912 + -6 Combine like terms: 6 + -6 = 0 0 + x = -5.949789912 + -6 x = -5.949789912 + -6 Combine like terms: -5.949789912 + -6 = -11.949789912 x = -11.949789912 Simplifying x = -11.949789912Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.050210088, -11.949789912}
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