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Simplifying 8x2 + 4.5x = 3600 Reorder the terms: 4.5x + 8x2 = 3600 Solving 4.5x + 8x2 = 3600 Solving for variable 'x'. Reorder the terms: -3600 + 4.5x + 8x2 = 3600 + -3600 Combine like terms: 3600 + -3600 = 0 -3600 + 4.5x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -450 + 0.5625x + x2 = 0 Move the constant term to the right: Add '450' to each side of the equation. -450 + 0.5625x + 450 + x2 = 0 + 450 Reorder the terms: -450 + 450 + 0.5625x + x2 = 0 + 450 Combine like terms: -450 + 450 = 0 0 + 0.5625x + x2 = 0 + 450 0.5625x + x2 = 0 + 450 Combine like terms: 0 + 450 = 450 0.5625x + x2 = 450 The x term is 0.5625x. Take half its coefficient (0.28125). Square it (0.0791015625) and add it to both sides. Add '0.0791015625' to each side of the equation. 0.5625x + 0.0791015625 + x2 = 450 + 0.0791015625 Reorder the terms: 0.0791015625 + 0.5625x + x2 = 450 + 0.0791015625 Combine like terms: 450 + 0.0791015625 = 450.0791015625 0.0791015625 + 0.5625x + x2 = 450.0791015625 Factor a perfect square on the left side: (x + 0.28125)(x + 0.28125) = 450.0791015625 Calculate the square root of the right side: 21.215067795 Break this problem into two subproblems by setting (x + 0.28125) equal to 21.215067795 and -21.215067795.Subproblem 1
x + 0.28125 = 21.215067795 Simplifying x + 0.28125 = 21.215067795 Reorder the terms: 0.28125 + x = 21.215067795 Solving 0.28125 + x = 21.215067795 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.28125' to each side of the equation. 0.28125 + -0.28125 + x = 21.215067795 + -0.28125 Combine like terms: 0.28125 + -0.28125 = 0.00000 0.00000 + x = 21.215067795 + -0.28125 x = 21.215067795 + -0.28125 Combine like terms: 21.215067795 + -0.28125 = 20.933817795 x = 20.933817795 Simplifying x = 20.933817795Subproblem 2
x + 0.28125 = -21.215067795 Simplifying x + 0.28125 = -21.215067795 Reorder the terms: 0.28125 + x = -21.215067795 Solving 0.28125 + x = -21.215067795 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.28125' to each side of the equation. 0.28125 + -0.28125 + x = -21.215067795 + -0.28125 Combine like terms: 0.28125 + -0.28125 = 0.00000 0.00000 + x = -21.215067795 + -0.28125 x = -21.215067795 + -0.28125 Combine like terms: -21.215067795 + -0.28125 = -21.496317795 x = -21.496317795 Simplifying x = -21.496317795Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.933817795, -21.496317795}
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