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Simplifying 5x(x + 6) = 3 Reorder the terms: 5x(6 + x) = 3 (6 * 5x + x * 5x) = 3 (30x + 5x2) = 3 Solving 30x + 5x2 = 3 Solving for variable 'x'. Reorder the terms: -3 + 30x + 5x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 30x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.6 + 6x + x2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + 6x + 0.6 + x2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + 6x + x2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + 6x + x2 = 0 + 0.6 6x + x2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 6x + x2 = 0.6 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 0.6 + 9 Reorder the terms: 9 + 6x + x2 = 0.6 + 9 Combine like terms: 0.6 + 9 = 9.6 9 + 6x + x2 = 9.6 Factor a perfect square on the left side: (x + 3)(x + 3) = 9.6 Calculate the square root of the right side: 3.098386677 Break this problem into two subproblems by setting (x + 3) equal to 3.098386677 and -3.098386677.Subproblem 1
x + 3 = 3.098386677 Simplifying x + 3 = 3.098386677 Reorder the terms: 3 + x = 3.098386677 Solving 3 + x = 3.098386677 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 3.098386677 + -3 Combine like terms: 3 + -3 = 0 0 + x = 3.098386677 + -3 x = 3.098386677 + -3 Combine like terms: 3.098386677 + -3 = 0.098386677 x = 0.098386677 Simplifying x = 0.098386677Subproblem 2
x + 3 = -3.098386677 Simplifying x + 3 = -3.098386677 Reorder the terms: 3 + x = -3.098386677 Solving 3 + x = -3.098386677 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -3.098386677 + -3 Combine like terms: 3 + -3 = 0 0 + x = -3.098386677 + -3 x = -3.098386677 + -3 Combine like terms: -3.098386677 + -3 = -6.098386677 x = -6.098386677 Simplifying x = -6.098386677Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.098386677, -6.098386677}
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