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Simplifying 8x2 + 300x = 180 Reorder the terms: 300x + 8x2 = 180 Solving 300x + 8x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + 300x + 8x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + 300x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-45 + 75x + 2x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-45 + 75x + 2x2)' equal to zero and attempt to solve: Simplifying -45 + 75x + 2x2 = 0 Solving -45 + 75x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -22.5 + 37.5x + x2 = 0 Move the constant term to the right: Add '22.5' to each side of the equation. -22.5 + 37.5x + 22.5 + x2 = 0 + 22.5 Reorder the terms: -22.5 + 22.5 + 37.5x + x2 = 0 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + 37.5x + x2 = 0 + 22.5 37.5x + x2 = 0 + 22.5 Combine like terms: 0 + 22.5 = 22.5 37.5x + x2 = 22.5 The x term is 37.5x. Take half its coefficient (18.75). Square it (351.5625) and add it to both sides. Add '351.5625' to each side of the equation. 37.5x + 351.5625 + x2 = 22.5 + 351.5625 Reorder the terms: 351.5625 + 37.5x + x2 = 22.5 + 351.5625 Combine like terms: 22.5 + 351.5625 = 374.0625 351.5625 + 37.5x + x2 = 374.0625 Factor a perfect square on the left side: (x + 18.75)(x + 18.75) = 374.0625 Calculate the square root of the right side: 19.340695437 Break this problem into two subproblems by setting (x + 18.75) equal to 19.340695437 and -19.340695437.Subproblem 1
x + 18.75 = 19.340695437 Simplifying x + 18.75 = 19.340695437 Reorder the terms: 18.75 + x = 19.340695437 Solving 18.75 + x = 19.340695437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.75' to each side of the equation. 18.75 + -18.75 + x = 19.340695437 + -18.75 Combine like terms: 18.75 + -18.75 = 0.00 0.00 + x = 19.340695437 + -18.75 x = 19.340695437 + -18.75 Combine like terms: 19.340695437 + -18.75 = 0.590695437 x = 0.590695437 Simplifying x = 0.590695437Subproblem 2
x + 18.75 = -19.340695437 Simplifying x + 18.75 = -19.340695437 Reorder the terms: 18.75 + x = -19.340695437 Solving 18.75 + x = -19.340695437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.75' to each side of the equation. 18.75 + -18.75 + x = -19.340695437 + -18.75 Combine like terms: 18.75 + -18.75 = 0.00 0.00 + x = -19.340695437 + -18.75 x = -19.340695437 + -18.75 Combine like terms: -19.340695437 + -18.75 = -38.090695437 x = -38.090695437 Simplifying x = -38.090695437Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.590695437, -38.090695437}Solution
x = {0.590695437, -38.090695437}
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