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Simplifying 49x2 + -150x + -400 = 0 Reorder the terms: -400 + -150x + 49x2 = 0 Solving -400 + -150x + 49x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -8.163265306 + -3.06122449x + x2 = 0 Move the constant term to the right: Add '8.163265306' to each side of the equation. -8.163265306 + -3.06122449x + 8.163265306 + x2 = 0 + 8.163265306 Reorder the terms: -8.163265306 + 8.163265306 + -3.06122449x + x2 = 0 + 8.163265306 Combine like terms: -8.163265306 + 8.163265306 = 0.000000000 0.000000000 + -3.06122449x + x2 = 0 + 8.163265306 -3.06122449x + x2 = 0 + 8.163265306 Combine like terms: 0 + 8.163265306 = 8.163265306 -3.06122449x + x2 = 8.163265306 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 = 8.163265306 + 2.342773845 Reorder the terms: 2.342773845 + -3.06122449x + x2 = 8.163265306 + 2.342773845 Combine like terms: 8.163265306 + 2.342773845 = 10.506039151 2.342773845 + -3.06122449x + x2 = 10.506039151 Factor a perfect square on the left side: (x + -1.530612245)(x + -1.530612245) = 10.506039151 Calculate the square root of the right side: 3.241302076 Break this problem into two subproblems by setting (x + -1.530612245) equal to 3.241302076 and -3.241302076.Subproblem 1
x + -1.530612245 = 3.241302076 Simplifying x + -1.530612245 = 3.241302076 Reorder the terms: -1.530612245 + x = 3.241302076 Solving -1.530612245 + x = 3.241302076 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 = 3.241302076 + 1.530612245 Combine like terms: -1.530612245 + 1.530612245 = 0.000000000 0.000000000 + x = 3.241302076 + 1.530612245 x = 3.241302076 + 1.530612245 Combine like terms: 3.241302076 + 1.530612245 = 4.771914321 x = 4.771914321 Simplifying x = 4.771914321Subproblem 2
x + -1.530612245 = -3.241302076 Simplifying x + -1.530612245 = -3.241302076 Reorder the terms: -1.530612245 + x = -3.241302076 Solving -1.530612245 + x = -3.241302076 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 = -3.241302076 + 1.530612245 Combine like terms: -1.530612245 + 1.530612245 = 0.000000000 0.000000000 + x = -3.241302076 + 1.530612245 x = -3.241302076 + 1.530612245 Combine like terms: -3.241302076 + 1.530612245 = -1.710689831 x = -1.710689831 Simplifying x = -1.710689831Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.771914321, -1.710689831}
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