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Simplifying x + (5x(x + 8)) = 124 Reorder the terms: x + (5x(8 + x)) = 124 x + ((8 * 5x + x * 5x)) = 124 x + ((40x + 5x2)) = 124 x + (40x + 5x2) = 124 Remove parenthesis around (40x + 5x2) x + 40x + 5x2 = 124 Combine like terms: x + 40x = 41x 41x + 5x2 = 124 Solving 41x + 5x2 = 124 Solving for variable 'x'. Reorder the terms: -124 + 41x + 5x2 = 124 + -124 Combine like terms: 124 + -124 = 0 -124 + 41x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -24.8 + 8.2x + x2 = 0 Move the constant term to the right: Add '24.8' to each side of the equation. -24.8 + 8.2x + 24.8 + x2 = 0 + 24.8 Reorder the terms: -24.8 + 24.8 + 8.2x + x2 = 0 + 24.8 Combine like terms: -24.8 + 24.8 = 0.0 0.0 + 8.2x + x2 = 0 + 24.8 8.2x + x2 = 0 + 24.8 Combine like terms: 0 + 24.8 = 24.8 8.2x + x2 = 24.8 The x term is 8.2x. Take half its coefficient (4.1). Square it (16.81) and add it to both sides. Add '16.81' to each side of the equation. 8.2x + 16.81 + x2 = 24.8 + 16.81 Reorder the terms: 16.81 + 8.2x + x2 = 24.8 + 16.81 Combine like terms: 24.8 + 16.81 = 41.61 16.81 + 8.2x + x2 = 41.61 Factor a perfect square on the left side: (x + 4.1)(x + 4.1) = 41.61 Calculate the square root of the right side: 6.450581369 Break this problem into two subproblems by setting (x + 4.1) equal to 6.450581369 and -6.450581369.Subproblem 1
x + 4.1 = 6.450581369 Simplifying x + 4.1 = 6.450581369 Reorder the terms: 4.1 + x = 6.450581369 Solving 4.1 + x = 6.450581369 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.1' to each side of the equation. 4.1 + -4.1 + x = 6.450581369 + -4.1 Combine like terms: 4.1 + -4.1 = 0.0 0.0 + x = 6.450581369 + -4.1 x = 6.450581369 + -4.1 Combine like terms: 6.450581369 + -4.1 = 2.350581369 x = 2.350581369 Simplifying x = 2.350581369Subproblem 2
x + 4.1 = -6.450581369 Simplifying x + 4.1 = -6.450581369 Reorder the terms: 4.1 + x = -6.450581369 Solving 4.1 + x = -6.450581369 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.1' to each side of the equation. 4.1 + -4.1 + x = -6.450581369 + -4.1 Combine like terms: 4.1 + -4.1 = 0.0 0.0 + x = -6.450581369 + -4.1 x = -6.450581369 + -4.1 Combine like terms: -6.450581369 + -4.1 = -10.550581369 x = -10.550581369 Simplifying x = -10.550581369Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.350581369, -10.550581369}
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