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Simplifying 8x2 + 4x = 261 Reorder the terms: 4x + 8x2 = 261 Solving 4x + 8x2 = 261 Solving for variable 'x'. Reorder the terms: -261 + 4x + 8x2 = 261 + -261 Combine like terms: 261 + -261 = 0 -261 + 4x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -32.625 + 0.5x + x2 = 0 Move the constant term to the right: Add '32.625' to each side of the equation. -32.625 + 0.5x + 32.625 + x2 = 0 + 32.625 Reorder the terms: -32.625 + 32.625 + 0.5x + x2 = 0 + 32.625 Combine like terms: -32.625 + 32.625 = 0.000 0.000 + 0.5x + x2 = 0 + 32.625 0.5x + x2 = 0 + 32.625 Combine like terms: 0 + 32.625 = 32.625 0.5x + x2 = 32.625 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 32.625 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 32.625 + 0.0625 Combine like terms: 32.625 + 0.0625 = 32.6875 0.0625 + 0.5x + x2 = 32.6875 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 32.6875 Calculate the square root of the right side: 5.717298313 Break this problem into two subproblems by setting (x + 0.25) equal to 5.717298313 and -5.717298313.Subproblem 1
x + 0.25 = 5.717298313 Simplifying x + 0.25 = 5.717298313 Reorder the terms: 0.25 + x = 5.717298313 Solving 0.25 + x = 5.717298313 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 5.717298313 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 5.717298313 + -0.25 x = 5.717298313 + -0.25 Combine like terms: 5.717298313 + -0.25 = 5.467298313 x = 5.467298313 Simplifying x = 5.467298313Subproblem 2
x + 0.25 = -5.717298313 Simplifying x + 0.25 = -5.717298313 Reorder the terms: 0.25 + x = -5.717298313 Solving 0.25 + x = -5.717298313 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -5.717298313 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -5.717298313 + -0.25 x = -5.717298313 + -0.25 Combine like terms: -5.717298313 + -0.25 = -5.967298313 x = -5.967298313 Simplifying x = -5.967298313Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.467298313, -5.967298313}
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