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Simplifying 4205 = 10x2 + 285x + 2700 Reorder the terms: 4205 = 2700 + 285x + 10x2 Solving 4205 = 2700 + 285x + 10x2 Solving for variable 'x'. Combine like terms: 4205 + -2700 = 1505 1505 + -285x + -10x2 = 2700 + 285x + 10x2 + -2700 + -285x + -10x2 Reorder the terms: 1505 + -285x + -10x2 = 2700 + -2700 + 285x + -285x + 10x2 + -10x2 Combine like terms: 2700 + -2700 = 0 1505 + -285x + -10x2 = 0 + 285x + -285x + 10x2 + -10x2 1505 + -285x + -10x2 = 285x + -285x + 10x2 + -10x2 Combine like terms: 285x + -285x = 0 1505 + -285x + -10x2 = 0 + 10x2 + -10x2 1505 + -285x + -10x2 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 1505 + -285x + -10x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(301 + -57x + -2x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(301 + -57x + -2x2)' equal to zero and attempt to solve: Simplifying 301 + -57x + -2x2 = 0 Solving 301 + -57x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -150.5 + 28.5x + x2 = 0 Move the constant term to the right: Add '150.5' to each side of the equation. -150.5 + 28.5x + 150.5 + x2 = 0 + 150.5 Reorder the terms: -150.5 + 150.5 + 28.5x + x2 = 0 + 150.5 Combine like terms: -150.5 + 150.5 = 0.0 0.0 + 28.5x + x2 = 0 + 150.5 28.5x + x2 = 0 + 150.5 Combine like terms: 0 + 150.5 = 150.5 28.5x + x2 = 150.5 The x term is 28.5x. Take half its coefficient (14.25). Square it (203.0625) and add it to both sides. Add '203.0625' to each side of the equation. 28.5x + 203.0625 + x2 = 150.5 + 203.0625 Reorder the terms: 203.0625 + 28.5x + x2 = 150.5 + 203.0625 Combine like terms: 150.5 + 203.0625 = 353.5625 203.0625 + 28.5x + x2 = 353.5625 Factor a perfect square on the left side: (x + 14.25)(x + 14.25) = 353.5625 Calculate the square root of the right side: 18.803257696 Break this problem into two subproblems by setting (x + 14.25) equal to 18.803257696 and -18.803257696.Subproblem 1
x + 14.25 = 18.803257696 Simplifying x + 14.25 = 18.803257696 Reorder the terms: 14.25 + x = 18.803257696 Solving 14.25 + x = 18.803257696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.25' to each side of the equation. 14.25 + -14.25 + x = 18.803257696 + -14.25 Combine like terms: 14.25 + -14.25 = 0.00 0.00 + x = 18.803257696 + -14.25 x = 18.803257696 + -14.25 Combine like terms: 18.803257696 + -14.25 = 4.553257696 x = 4.553257696 Simplifying x = 4.553257696Subproblem 2
x + 14.25 = -18.803257696 Simplifying x + 14.25 = -18.803257696 Reorder the terms: 14.25 + x = -18.803257696 Solving 14.25 + x = -18.803257696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.25' to each side of the equation. 14.25 + -14.25 + x = -18.803257696 + -14.25 Combine like terms: 14.25 + -14.25 = 0.00 0.00 + x = -18.803257696 + -14.25 x = -18.803257696 + -14.25 Combine like terms: -18.803257696 + -14.25 = -33.053257696 x = -33.053257696 Simplifying x = -33.053257696Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.553257696, -33.053257696}Solution
x = {4.553257696, -33.053257696}
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