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Simplifying 490x2 + -1500x + -200 = 0 Reorder the terms: -200 + -1500x + 490x2 = 0 Solving -200 + -1500x + 490x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '10'. 10(-20 + -150x + 49x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-20 + -150x + 49x2)' equal to zero and attempt to solve: Simplifying -20 + -150x + 49x2 = 0 Solving -20 + -150x + 49x2 = 0 Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -0.4081632653 + -3.06122449x + x2 = 0 Move the constant term to the right: Add '0.4081632653' to each side of the equation. -0.4081632653 + -3.06122449x + 0.4081632653 + x2 = 0 + 0.4081632653 Reorder the terms: -0.4081632653 + 0.4081632653 + -3.06122449x + x2 = 0 + 0.4081632653 Combine like terms: -0.4081632653 + 0.4081632653 = 0.0000000000 0.0000000000 + -3.06122449x + x2 = 0 + 0.4081632653 -3.06122449x + x2 = 0 + 0.4081632653 Combine like terms: 0 + 0.4081632653 = 0.4081632653 -3.06122449x + x2 = 0.4081632653 The x term is -3.06122449x. Take half its coefficient (-1.530612245). Square it (2.342773845) and add it to both sides. Add '2.342773845' to each side of the equation. -3.06122449x + 2.342773845 + x2 = 0.4081632653 + 2.342773845 Reorder the terms: 2.342773845 + -3.06122449x + x2 = 0.4081632653 + 2.342773845 Combine like terms: 0.4081632653 + 2.342773845 = 2.7509371103 2.342773845 + -3.06122449x + x2 = 2.7509371103 Factor a perfect square on the left side: (x + -1.530612245)(x + -1.530612245) = 2.7509371103 Calculate the square root of the right side: 1.65859492 Break this problem into two subproblems by setting (x + -1.530612245) equal to 1.65859492 and -1.65859492.Subproblem 1
x + -1.530612245 = 1.65859492 Simplifying x + -1.530612245 = 1.65859492 Reorder the terms: -1.530612245 + x = 1.65859492 Solving -1.530612245 + x = 1.65859492 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.530612245' to each side of the equation. -1.530612245 + 1.530612245 + x = 1.65859492 + 1.530612245 Combine like terms: -1.530612245 + 1.530612245 = 0.000000000 0.000000000 + x = 1.65859492 + 1.530612245 x = 1.65859492 + 1.530612245 Combine like terms: 1.65859492 + 1.530612245 = 3.189207165 x = 3.189207165 Simplifying x = 3.189207165Subproblem 2
x + -1.530612245 = -1.65859492 Simplifying x + -1.530612245 = -1.65859492 Reorder the terms: -1.530612245 + x = -1.65859492 Solving -1.530612245 + x = -1.65859492 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.530612245' to each side of the equation. -1.530612245 + 1.530612245 + x = -1.65859492 + 1.530612245 Combine like terms: -1.530612245 + 1.530612245 = 0.000000000 0.000000000 + x = -1.65859492 + 1.530612245 x = -1.65859492 + 1.530612245 Combine like terms: -1.65859492 + 1.530612245 = -0.127982675 x = -0.127982675 Simplifying x = -0.127982675Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.189207165, -0.127982675}Solution
x = {3.189207165, -0.127982675}
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