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Simplifying 5(2x + 1) * 6x = 13 Reorder the terms: 5(1 + 2x) * 6x = 13 Reorder the terms for easier multiplication: 5 * 6x(1 + 2x) = 13 Multiply 5 * 6 30x(1 + 2x) = 13 (1 * 30x + 2x * 30x) = 13 (30x + 60x2) = 13 Solving 30x + 60x2 = 13 Solving for variable 'x'. Reorder the terms: -13 + 30x + 60x2 = 13 + -13 Combine like terms: 13 + -13 = 0 -13 + 30x + 60x2 = 0 Begin completing the square. Divide all terms by 60 the coefficient of the squared term: Divide each side by '60'. -0.2166666667 + 0.5x + x2 = 0.0 Move the constant term to the right: Add '0.2166666667' to each side of the equation. -0.2166666667 + 0.5x + 0.2166666667 + x2 = 0.0 + 0.2166666667 Reorder the terms: -0.2166666667 + 0.2166666667 + 0.5x + x2 = 0.0 + 0.2166666667 Combine like terms: -0.2166666667 + 0.2166666667 = 0.0000000000 0.0000000000 + 0.5x + x2 = 0.0 + 0.2166666667 0.5x + x2 = 0.0 + 0.2166666667 Combine like terms: 0.0 + 0.2166666667 = 0.2166666667 0.5x + x2 = 0.2166666667 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 0.2166666667 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 0.2166666667 + 0.0625 Combine like terms: 0.2166666667 + 0.0625 = 0.2791666667 0.0625 + 0.5x + x2 = 0.2791666667 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 0.2791666667 Calculate the square root of the right side: 0.52836225 Break this problem into two subproblems by setting (x + 0.25) equal to 0.52836225 and -0.52836225.Subproblem 1
x + 0.25 = 0.52836225 Simplifying x + 0.25 = 0.52836225 Reorder the terms: 0.25 + x = 0.52836225 Solving 0.25 + x = 0.52836225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 0.52836225 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 0.52836225 + -0.25 x = 0.52836225 + -0.25 Combine like terms: 0.52836225 + -0.25 = 0.27836225 x = 0.27836225 Simplifying x = 0.27836225Subproblem 2
x + 0.25 = -0.52836225 Simplifying x + 0.25 = -0.52836225 Reorder the terms: 0.25 + x = -0.52836225 Solving 0.25 + x = -0.52836225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -0.52836225 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -0.52836225 + -0.25 x = -0.52836225 + -0.25 Combine like terms: -0.52836225 + -0.25 = -0.77836225 x = -0.77836225 Simplifying x = -0.77836225Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.27836225, -0.77836225}
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