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Simplifying 5x(x + 8) = 2x + 15 Reorder the terms: 5x(8 + x) = 2x + 15 (8 * 5x + x * 5x) = 2x + 15 (40x + 5x2) = 2x + 15 Reorder the terms: 40x + 5x2 = 15 + 2x Solving 40x + 5x2 = 15 + 2x Solving for variable 'x'. Reorder the terms: -15 + 40x + -2x + 5x2 = 15 + 2x + -15 + -2x Combine like terms: 40x + -2x = 38x -15 + 38x + 5x2 = 15 + 2x + -15 + -2x Reorder the terms: -15 + 38x + 5x2 = 15 + -15 + 2x + -2x Combine like terms: 15 + -15 = 0 -15 + 38x + 5x2 = 0 + 2x + -2x -15 + 38x + 5x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -15 + 38x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3 + 7.6x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 7.6x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 7.6x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 7.6x + x2 = 0 + 3 7.6x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 7.6x + x2 = 3 The x term is 7.6x. Take half its coefficient (3.8). Square it (14.44) and add it to both sides. Add '14.44' to each side of the equation. 7.6x + 14.44 + x2 = 3 + 14.44 Reorder the terms: 14.44 + 7.6x + x2 = 3 + 14.44 Combine like terms: 3 + 14.44 = 17.44 14.44 + 7.6x + x2 = 17.44 Factor a perfect square on the left side: (x + 3.8)(x + 3.8) = 17.44 Calculate the square root of the right side: 4.176122604 Break this problem into two subproblems by setting (x + 3.8) equal to 4.176122604 and -4.176122604.Subproblem 1
x + 3.8 = 4.176122604 Simplifying x + 3.8 = 4.176122604 Reorder the terms: 3.8 + x = 4.176122604 Solving 3.8 + x = 4.176122604 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.8' to each side of the equation. 3.8 + -3.8 + x = 4.176122604 + -3.8 Combine like terms: 3.8 + -3.8 = 0.0 0.0 + x = 4.176122604 + -3.8 x = 4.176122604 + -3.8 Combine like terms: 4.176122604 + -3.8 = 0.376122604 x = 0.376122604 Simplifying x = 0.376122604Subproblem 2
x + 3.8 = -4.176122604 Simplifying x + 3.8 = -4.176122604 Reorder the terms: 3.8 + x = -4.176122604 Solving 3.8 + x = -4.176122604 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.8' to each side of the equation. 3.8 + -3.8 + x = -4.176122604 + -3.8 Combine like terms: 3.8 + -3.8 = 0.0 0.0 + x = -4.176122604 + -3.8 x = -4.176122604 + -3.8 Combine like terms: -4.176122604 + -3.8 = -7.976122604 x = -7.976122604 Simplifying x = -7.976122604Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.376122604, -7.976122604}
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