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Simplifying 75x2 + 210x + 132 = 0 Reorder the terms: 132 + 210x + 75x2 = 0 Solving 132 + 210x + 75x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(44 + 70x + 25x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(44 + 70x + 25x2)' equal to zero and attempt to solve: Simplifying 44 + 70x + 25x2 = 0 Solving 44 + 70x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 1.76 + 2.8x + x2 = 0 Move the constant term to the right: Add '-1.76' to each side of the equation. 1.76 + 2.8x + -1.76 + x2 = 0 + -1.76 Reorder the terms: 1.76 + -1.76 + 2.8x + x2 = 0 + -1.76 Combine like terms: 1.76 + -1.76 = 0.00 0.00 + 2.8x + x2 = 0 + -1.76 2.8x + x2 = 0 + -1.76 Combine like terms: 0 + -1.76 = -1.76 2.8x + x2 = -1.76 The x term is 2.8x. Take half its coefficient (1.4). Square it (1.96) and add it to both sides. Add '1.96' to each side of the equation. 2.8x + 1.96 + x2 = -1.76 + 1.96 Reorder the terms: 1.96 + 2.8x + x2 = -1.76 + 1.96 Combine like terms: -1.76 + 1.96 = 0.2 1.96 + 2.8x + x2 = 0.2 Factor a perfect square on the left side: (x + 1.4)(x + 1.4) = 0.2 Calculate the square root of the right side: 0.447213596 Break this problem into two subproblems by setting (x + 1.4) equal to 0.447213596 and -0.447213596.Subproblem 1
x + 1.4 = 0.447213596 Simplifying x + 1.4 = 0.447213596 Reorder the terms: 1.4 + x = 0.447213596 Solving 1.4 + x = 0.447213596 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.4' to each side of the equation. 1.4 + -1.4 + x = 0.447213596 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + x = 0.447213596 + -1.4 x = 0.447213596 + -1.4 Combine like terms: 0.447213596 + -1.4 = -0.952786404 x = -0.952786404 Simplifying x = -0.952786404Subproblem 2
x + 1.4 = -0.447213596 Simplifying x + 1.4 = -0.447213596 Reorder the terms: 1.4 + x = -0.447213596 Solving 1.4 + x = -0.447213596 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.4' to each side of the equation. 1.4 + -1.4 + x = -0.447213596 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + x = -0.447213596 + -1.4 x = -0.447213596 + -1.4 Combine like terms: -0.447213596 + -1.4 = -1.847213596 x = -1.847213596 Simplifying x = -1.847213596Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.952786404, -1.847213596}Solution
x = {-0.952786404, -1.847213596}
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