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Simplifying 41 = 5x(2x + 3) Reorder the terms: 41 = 5x(3 + 2x) 41 = (3 * 5x + 2x * 5x) 41 = (15x + 10x2) Solving 41 = 15x + 10x2 Solving for variable 'x'. Reorder the terms: 41 + -15x + -10x2 = 15x + -15x + 10x2 + -10x2 Combine like terms: 15x + -15x = 0 41 + -15x + -10x2 = 0 + 10x2 + -10x2 41 + -15x + -10x2 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 41 + -15x + -10x2 = 0 Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -4.1 + 1.5x + x2 = 0 Move the constant term to the right: Add '4.1' to each side of the equation. -4.1 + 1.5x + 4.1 + x2 = 0 + 4.1 Reorder the terms: -4.1 + 4.1 + 1.5x + x2 = 0 + 4.1 Combine like terms: -4.1 + 4.1 = 0.0 0.0 + 1.5x + x2 = 0 + 4.1 1.5x + x2 = 0 + 4.1 Combine like terms: 0 + 4.1 = 4.1 1.5x + x2 = 4.1 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 4.1 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 4.1 + 0.5625 Combine like terms: 4.1 + 0.5625 = 4.6625 0.5625 + 1.5x + x2 = 4.6625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 4.6625 Calculate the square root of the right side: 2.159282288 Break this problem into two subproblems by setting (x + 0.75) equal to 2.159282288 and -2.159282288.Subproblem 1
x + 0.75 = 2.159282288 Simplifying x + 0.75 = 2.159282288 Reorder the terms: 0.75 + x = 2.159282288 Solving 0.75 + x = 2.159282288 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 2.159282288 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 2.159282288 + -0.75 x = 2.159282288 + -0.75 Combine like terms: 2.159282288 + -0.75 = 1.409282288 x = 1.409282288 Simplifying x = 1.409282288Subproblem 2
x + 0.75 = -2.159282288 Simplifying x + 0.75 = -2.159282288 Reorder the terms: 0.75 + x = -2.159282288 Solving 0.75 + x = -2.159282288 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -2.159282288 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -2.159282288 + -0.75 x = -2.159282288 + -0.75 Combine like terms: -2.159282288 + -0.75 = -2.909282288 x = -2.909282288 Simplifying x = -2.909282288Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.409282288, -2.909282288}
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