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Simplifying 2x(x + 8) + 15 = 0 Reorder the terms: 2x(8 + x) + 15 = 0 (8 * 2x + x * 2x) + 15 = 0 (16x + 2x2) + 15 = 0 Reorder the terms: 15 + 16x + 2x2 = 0 Solving 15 + 16x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 7.5 + 8x + x2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + 8x + -7.5 + x2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + 8x + x2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + 8x + x2 = 0 + -7.5 8x + x2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 8x + x2 = -7.5 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 = -7.5 + 16 Reorder the terms: 16 + 8x + x2 = -7.5 + 16 Combine like terms: -7.5 + 16 = 8.5 16 + 8x + x2 = 8.5 Factor a perfect square on the left side: (x + 4)(x + 4) = 8.5 Calculate the square root of the right side: 2.915475947 Break this problem into two subproblems by setting (x + 4) equal to 2.915475947 and -2.915475947.Subproblem 1
x + 4 = 2.915475947 Simplifying x + 4 = 2.915475947 Reorder the terms: 4 + x = 2.915475947 Solving 4 + x = 2.915475947 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 = 2.915475947 + -4 Combine like terms: 4 + -4 = 0 0 + x = 2.915475947 + -4 x = 2.915475947 + -4 Combine like terms: 2.915475947 + -4 = -1.084524053 x = -1.084524053 Simplifying x = -1.084524053Subproblem 2
x + 4 = -2.915475947 Simplifying x + 4 = -2.915475947 Reorder the terms: 4 + x = -2.915475947 Solving 4 + x = -2.915475947 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 = -2.915475947 + -4 Combine like terms: 4 + -4 = 0 0 + x = -2.915475947 + -4 x = -2.915475947 + -4 Combine like terms: -2.915475947 + -4 = -6.915475947 x = -6.915475947 Simplifying x = -6.915475947Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.084524053, -6.915475947}
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