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Simplifying 98x2 + -280x + 40 = 0 Reorder the terms: 40 + -280x + 98x2 = 0 Solving 40 + -280x + 98x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(20 + -140x + 49x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(20 + -140x + 49x2)' equal to zero and attempt to solve: Simplifying 20 + -140x + 49x2 = 0 Solving 20 + -140x + 49x2 = 0 Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. 0.4081632653 + -2.857142857x + x2 = 0 Move the constant term to the right: Add '-0.4081632653' to each side of the equation. 0.4081632653 + -2.857142857x + -0.4081632653 + x2 = 0 + -0.4081632653 Reorder the terms: 0.4081632653 + -0.4081632653 + -2.857142857x + x2 = 0 + -0.4081632653 Combine like terms: 0.4081632653 + -0.4081632653 = 0.0000000000 0.0000000000 + -2.857142857x + x2 = 0 + -0.4081632653 -2.857142857x + x2 = 0 + -0.4081632653 Combine like terms: 0 + -0.4081632653 = -0.4081632653 -2.857142857x + x2 = -0.4081632653 The x term is -2.857142857x. Take half its coefficient (-1.428571429). Square it (2.040816328) and add it to both sides. Add '2.040816328' to each side of the equation. -2.857142857x + 2.040816328 + x2 = -0.4081632653 + 2.040816328 Reorder the terms: 2.040816328 + -2.857142857x + x2 = -0.4081632653 + 2.040816328 Combine like terms: -0.4081632653 + 2.040816328 = 1.6326530627 2.040816328 + -2.857142857x + x2 = 1.6326530627 Factor a perfect square on the left side: (x + -1.428571429)(x + -1.428571429) = 1.6326530627 Calculate the square root of the right side: 1.277753131 Break this problem into two subproblems by setting (x + -1.428571429) equal to 1.277753131 and -1.277753131.Subproblem 1
x + -1.428571429 = 1.277753131 Simplifying x + -1.428571429 = 1.277753131 Reorder the terms: -1.428571429 + x = 1.277753131 Solving -1.428571429 + x = 1.277753131 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + x = 1.277753131 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + x = 1.277753131 + 1.428571429 x = 1.277753131 + 1.428571429 Combine like terms: 1.277753131 + 1.428571429 = 2.70632456 x = 2.70632456 Simplifying x = 2.70632456Subproblem 2
x + -1.428571429 = -1.277753131 Simplifying x + -1.428571429 = -1.277753131 Reorder the terms: -1.428571429 + x = -1.277753131 Solving -1.428571429 + x = -1.277753131 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + x = -1.277753131 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + x = -1.277753131 + 1.428571429 x = -1.277753131 + 1.428571429 Combine like terms: -1.277753131 + 1.428571429 = 0.150818298 x = 0.150818298 Simplifying x = 0.150818298Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.70632456, 0.150818298}Solution
x = {2.70632456, 0.150818298}
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