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Simplifying 81x2 + -126x + 49 = 0.25 Reorder the terms: 49 + -126x + 81x2 = 0.25 Solving 49 + -126x + 81x2 = 0.25 Solving for variable 'x'. Reorder the terms: 49 + -0.25 + -126x + 81x2 = 0.25 + -0.25 Combine like terms: 49 + -0.25 = 48.75 48.75 + -126x + 81x2 = 0.25 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 48.75 + -126x + 81x2 = 0.00 Begin completing the square. Divide all terms by 81 the coefficient of the squared term: Divide each side by '81'. 0.6018518519 + -1.555555556x + x2 = 0.00 Move the constant term to the right: Add '-0.6018518519' to each side of the equation. 0.6018518519 + -1.555555556x + -0.6018518519 + x2 = 0.00 + -0.6018518519 Reorder the terms: 0.6018518519 + -0.6018518519 + -1.555555556x + x2 = 0.00 + -0.6018518519 Combine like terms: 0.6018518519 + -0.6018518519 = 0.0000000000 0.0000000000 + -1.555555556x + x2 = 0.00 + -0.6018518519 -1.555555556x + x2 = 0.00 + -0.6018518519 Combine like terms: 0.00 + -0.6018518519 = -0.6018518519 -1.555555556x + x2 = -0.6018518519 The x term is -1.555555556x. Take half its coefficient (-0.777777778). Square it (0.6049382720) and add it to both sides. Add '0.6049382720' to each side of the equation. -1.555555556x + 0.6049382720 + x2 = -0.6018518519 + 0.6049382720 Reorder the terms: 0.6049382720 + -1.555555556x + x2 = -0.6018518519 + 0.6049382720 Combine like terms: -0.6018518519 + 0.6049382720 = 0.0030864201 0.6049382720 + -1.555555556x + x2 = 0.0030864201 Factor a perfect square on the left side: (x + -0.777777778)(x + -0.777777778) = 0.0030864201 Calculate the square root of the right side: 0.055555559 Break this problem into two subproblems by setting (x + -0.777777778) equal to 0.055555559 and -0.055555559.Subproblem 1
x + -0.777777778 = 0.055555559 Simplifying x + -0.777777778 = 0.055555559 Reorder the terms: -0.777777778 + x = 0.055555559 Solving -0.777777778 + x = 0.055555559 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.777777778' to each side of the equation. -0.777777778 + 0.777777778 + x = 0.055555559 + 0.777777778 Combine like terms: -0.777777778 + 0.777777778 = 0.000000000 0.000000000 + x = 0.055555559 + 0.777777778 x = 0.055555559 + 0.777777778 Combine like terms: 0.055555559 + 0.777777778 = 0.833333337 x = 0.833333337 Simplifying x = 0.833333337Subproblem 2
x + -0.777777778 = -0.055555559 Simplifying x + -0.777777778 = -0.055555559 Reorder the terms: -0.777777778 + x = -0.055555559 Solving -0.777777778 + x = -0.055555559 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.777777778' to each side of the equation. -0.777777778 + 0.777777778 + x = -0.055555559 + 0.777777778 Combine like terms: -0.777777778 + 0.777777778 = 0.000000000 0.000000000 + x = -0.055555559 + 0.777777778 x = -0.055555559 + 0.777777778 Combine like terms: -0.055555559 + 0.777777778 = 0.722222219 x = 0.722222219 Simplifying x = 0.722222219Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.833333337, 0.722222219}
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