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Simplifying 5x(8 + x) = 3 (8 * 5x + x * 5x) = 3 (40x + 5x2) = 3 Solving 40x + 5x2 = 3 Solving for variable 'x'. Reorder the terms: -3 + 40x + 5x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 40x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.6 + 8x + x2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + 8x + 0.6 + x2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + 8x + x2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + 8x + x2 = 0 + 0.6 8x + x2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 8x + x2 = 0.6 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 0.6 + 16 Reorder the terms: 16 + 8x + x2 = 0.6 + 16 Combine like terms: 0.6 + 16 = 16.6 16 + 8x + x2 = 16.6 Factor a perfect square on the left side: (x + 4)(x + 4) = 16.6 Calculate the square root of the right side: 4.074309757 Break this problem into two subproblems by setting (x + 4) equal to 4.074309757 and -4.074309757.Subproblem 1
x + 4 = 4.074309757 Simplifying x + 4 = 4.074309757 Reorder the terms: 4 + x = 4.074309757 Solving 4 + x = 4.074309757 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 4.074309757 + -4 Combine like terms: 4 + -4 = 0 0 + x = 4.074309757 + -4 x = 4.074309757 + -4 Combine like terms: 4.074309757 + -4 = 0.074309757 x = 0.074309757 Simplifying x = 0.074309757Subproblem 2
x + 4 = -4.074309757 Simplifying x + 4 = -4.074309757 Reorder the terms: 4 + x = -4.074309757 Solving 4 + x = -4.074309757 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -4.074309757 + -4 Combine like terms: 4 + -4 = 0 0 + x = -4.074309757 + -4 x = -4.074309757 + -4 Combine like terms: -4.074309757 + -4 = -8.074309757 x = -8.074309757 Simplifying x = -8.074309757Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.074309757, -8.074309757}
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