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Simplifying 0.5(4x + 2) * x = 1296 Reorder the terms: 0.5(2 + 4x) * x = 1296 Reorder the terms for easier multiplication: 0.5x(2 + 4x) = 1296 (2 * 0.5x + 4x * 0.5x) = 1296 (1x + 2x2) = 1296 Solving 1x + 2x2 = 1296 Solving for variable 'x'. Reorder the terms: -1296 + 1x + 2x2 = 1296 + -1296 Combine like terms: 1296 + -1296 = 0 -1296 + 1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -648 + 0.5x + x2 = 0 Move the constant term to the right: Add '648' to each side of the equation. -648 + 0.5x + 648 + x2 = 0 + 648 Reorder the terms: -648 + 648 + 0.5x + x2 = 0 + 648 Combine like terms: -648 + 648 = 0 0 + 0.5x + x2 = 0 + 648 0.5x + x2 = 0 + 648 Combine like terms: 0 + 648 = 648 0.5x + x2 = 648 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 = 648 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 648 + 0.0625 Combine like terms: 648 + 0.0625 = 648.0625 0.0625 + 0.5x + x2 = 648.0625 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 648.0625 Calculate the square root of the right side: 25.457071709 Break this problem into two subproblems by setting (x + 0.25) equal to 25.457071709 and -25.457071709.Subproblem 1
x + 0.25 = 25.457071709 Simplifying x + 0.25 = 25.457071709 Reorder the terms: 0.25 + x = 25.457071709 Solving 0.25 + x = 25.457071709 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 = 25.457071709 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 25.457071709 + -0.25 x = 25.457071709 + -0.25 Combine like terms: 25.457071709 + -0.25 = 25.207071709 x = 25.207071709 Simplifying x = 25.207071709Subproblem 2
x + 0.25 = -25.457071709 Simplifying x + 0.25 = -25.457071709 Reorder the terms: 0.25 + x = -25.457071709 Solving 0.25 + x = -25.457071709 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 = -25.457071709 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -25.457071709 + -0.25 x = -25.457071709 + -0.25 Combine like terms: -25.457071709 + -0.25 = -25.707071709 x = -25.707071709 Simplifying x = -25.707071709Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.207071709, -25.707071709}
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