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Simplifying 49x2 + -255x + 20 = 0 Reorder the terms: 20 + -255x + 49x2 = 0 Solving 20 + -255x + 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'. 0.4081632653 + -5.204081633x + x2 = 0 Move the constant term to the right: Add '-0.4081632653' to each side of the equation. 0.4081632653 + -5.204081633x + -0.4081632653 + x2 = 0 + -0.4081632653 Reorder the terms: 0.4081632653 + -0.4081632653 + -5.204081633x + x2 = 0 + -0.4081632653 Combine like terms: 0.4081632653 + -0.4081632653 = 0.0000000000 0.0000000000 + -5.204081633x + x2 = 0 + -0.4081632653 -5.204081633x + x2 = 0 + -0.4081632653 Combine like terms: 0 + -0.4081632653 = -0.4081632653 -5.204081633x + x2 = -0.4081632653 The x term is -5.204081633x. Take half its coefficient (-2.602040817). Square it (6.770616413) and add it to both sides. Add '6.770616413' to each side of the equation. -5.204081633x + 6.770616413 + x2 = -0.4081632653 + 6.770616413 Reorder the terms: 6.770616413 + -5.204081633x + x2 = -0.4081632653 + 6.770616413 Combine like terms: -0.4081632653 + 6.770616413 = 6.3624531477 6.770616413 + -5.204081633x + x2 = 6.3624531477 Factor a perfect square on the left side: (x + -2.602040817)(x + -2.602040817) = 6.3624531477 Calculate the square root of the right side: 2.522390364 Break this problem into two subproblems by setting (x + -2.602040817) equal to 2.522390364 and -2.522390364.Subproblem 1
x + -2.602040817 = 2.522390364 Simplifying x + -2.602040817 = 2.522390364 Reorder the terms: -2.602040817 + x = 2.522390364 Solving -2.602040817 + x = 2.522390364 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.602040817' to each side of the equation. -2.602040817 + 2.602040817 + x = 2.522390364 + 2.602040817 Combine like terms: -2.602040817 + 2.602040817 = 0.000000000 0.000000000 + x = 2.522390364 + 2.602040817 x = 2.522390364 + 2.602040817 Combine like terms: 2.522390364 + 2.602040817 = 5.124431181 x = 5.124431181 Simplifying x = 5.124431181Subproblem 2
x + -2.602040817 = -2.522390364 Simplifying x + -2.602040817 = -2.522390364 Reorder the terms: -2.602040817 + x = -2.522390364 Solving -2.602040817 + x = -2.522390364 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.602040817' to each side of the equation. -2.602040817 + 2.602040817 + x = -2.522390364 + 2.602040817 Combine like terms: -2.602040817 + 2.602040817 = 0.000000000 0.000000000 + x = -2.522390364 + 2.602040817 x = -2.522390364 + 2.602040817 Combine like terms: -2.522390364 + 2.602040817 = 0.079650453 x = 0.079650453 Simplifying x = 0.079650453Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.124431181, 0.079650453}
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