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Simplifying 2x(x + 4) = 9 Reorder the terms: 2x(4 + x) = 9 (4 * 2x + x * 2x) = 9 (8x + 2x2) = 9 Solving 8x + 2x2 = 9 Solving for variable 'x'. Reorder the terms: -9 + 8x + 2x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + 8x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4.5 + 4x + x2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + 4x + 4.5 + x2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + 4x + x2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + 4x + x2 = 0 + 4.5 4x + x2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 4x + x2 = 4.5 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 4.5 + 4 Reorder the terms: 4 + 4x + x2 = 4.5 + 4 Combine like terms: 4.5 + 4 = 8.5 4 + 4x + x2 = 8.5 Factor a perfect square on the left side: (x + 2)(x + 2) = 8.5 Calculate the square root of the right side: 2.915475947 Break this problem into two subproblems by setting (x + 2) equal to 2.915475947 and -2.915475947.Subproblem 1
x + 2 = 2.915475947 Simplifying x + 2 = 2.915475947 Reorder the terms: 2 + x = 2.915475947 Solving 2 + x = 2.915475947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 2.915475947 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.915475947 + -2 x = 2.915475947 + -2 Combine like terms: 2.915475947 + -2 = 0.915475947 x = 0.915475947 Simplifying x = 0.915475947Subproblem 2
x + 2 = -2.915475947 Simplifying x + 2 = -2.915475947 Reorder the terms: 2 + x = -2.915475947 Solving 2 + x = -2.915475947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -2.915475947 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.915475947 + -2 x = -2.915475947 + -2 Combine like terms: -2.915475947 + -2 = -4.915475947 x = -4.915475947 Simplifying x = -4.915475947Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.915475947, -4.915475947}
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