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Simplifying 5x(x + 1) = 46 Reorder the terms: 5x(1 + x) = 46 (1 * 5x + x * 5x) = 46 (5x + 5x2) = 46 Solving 5x + 5x2 = 46 Solving for variable 'x'. Reorder the terms: -46 + 5x + 5x2 = 46 + -46 Combine like terms: 46 + -46 = 0 -46 + 5x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -9.2 + x + x2 = 0 Move the constant term to the right: Add '9.2' to each side of the equation. -9.2 + x + 9.2 + x2 = 0 + 9.2 Reorder the terms: -9.2 + 9.2 + x + x2 = 0 + 9.2 Combine like terms: -9.2 + 9.2 = 0.0 0.0 + x + x2 = 0 + 9.2 x + x2 = 0 + 9.2 Combine like terms: 0 + 9.2 = 9.2 x + x2 = 9.2 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 9.2 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 9.2 + 0.25 Combine like terms: 9.2 + 0.25 = 9.45 1.25 + x2 = 9.45 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 9.45 Calculate the square root of the right side: 3.07408523 Break this problem into two subproblems by setting (x + 0.5) equal to 3.07408523 and -3.07408523.Subproblem 1
x + 0.5 = 3.07408523 Simplifying x + 0.5 = 3.07408523 Reorder the terms: 0.5 + x = 3.07408523 Solving 0.5 + x = 3.07408523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 3.07408523 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 3.07408523 + -0.5 x = 3.07408523 + -0.5 Combine like terms: 3.07408523 + -0.5 = 2.57408523 x = 2.57408523 Simplifying x = 2.57408523Subproblem 2
x + 0.5 = -3.07408523 Simplifying x + 0.5 = -3.07408523 Reorder the terms: 0.5 + x = -3.07408523 Solving 0.5 + x = -3.07408523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -3.07408523 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -3.07408523 + -0.5 x = -3.07408523 + -0.5 Combine like terms: -3.07408523 + -0.5 = -3.57408523 x = -3.57408523 Simplifying x = -3.57408523Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.57408523, -3.57408523}
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