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Simplifying 5(2x + 1) * 3x = 44 Reorder the terms: 5(1 + 2x) * 3x = 44 Reorder the terms for easier multiplication: 5 * 3x(1 + 2x) = 44 Multiply 5 * 3 15x(1 + 2x) = 44 (1 * 15x + 2x * 15x) = 44 (15x + 30x2) = 44 Solving 15x + 30x2 = 44 Solving for variable 'x'. Reorder the terms: -44 + 15x + 30x2 = 44 + -44 Combine like terms: 44 + -44 = 0 -44 + 15x + 30x2 = 0 Begin completing the square. Divide all terms by 30 the coefficient of the squared term: Divide each side by '30'. -1.466666667 + 0.5x + x2 = 0.0 Move the constant term to the right: Add '1.466666667' to each side of the equation. -1.466666667 + 0.5x + 1.466666667 + x2 = 0.0 + 1.466666667 Reorder the terms: -1.466666667 + 1.466666667 + 0.5x + x2 = 0.0 + 1.466666667 Combine like terms: -1.466666667 + 1.466666667 = 0.000000000 0.000000000 + 0.5x + x2 = 0.0 + 1.466666667 0.5x + x2 = 0.0 + 1.466666667 Combine like terms: 0.0 + 1.466666667 = 1.466666667 0.5x + x2 = 1.466666667 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 = 1.466666667 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 1.466666667 + 0.0625 Combine like terms: 1.466666667 + 0.0625 = 1.529166667 0.0625 + 0.5x + x2 = 1.529166667 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 1.529166667 Calculate the square root of the right side: 1.236594787 Break this problem into two subproblems by setting (x + 0.25) equal to 1.236594787 and -1.236594787.Subproblem 1
x + 0.25 = 1.236594787 Simplifying x + 0.25 = 1.236594787 Reorder the terms: 0.25 + x = 1.236594787 Solving 0.25 + x = 1.236594787 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 = 1.236594787 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 1.236594787 + -0.25 x = 1.236594787 + -0.25 Combine like terms: 1.236594787 + -0.25 = 0.986594787 x = 0.986594787 Simplifying x = 0.986594787Subproblem 2
x + 0.25 = -1.236594787 Simplifying x + 0.25 = -1.236594787 Reorder the terms: 0.25 + x = -1.236594787 Solving 0.25 + x = -1.236594787 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 = -1.236594787 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -1.236594787 + -0.25 x = -1.236594787 + -0.25 Combine like terms: -1.236594787 + -0.25 = -1.486594787 x = -1.486594787 Simplifying x = -1.486594787Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.986594787, -1.486594787}
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