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Simplifying -4.90x2 + -2.25x + 1.92 = 0 Reorder the terms: 1.92 + -2.25x + -4.90x2 = 0 Solving 1.92 + -2.25x + -4.90x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4.90 the coefficient of the squared term: Divide each side by '-4.90'. -0.3918367347 + 0.4591836735x + x2 = 0 Move the constant term to the right: Add '0.3918367347' to each side of the equation. -0.3918367347 + 0.4591836735x + 0.3918367347 + x2 = 0 + 0.3918367347 Reorder the terms: -0.3918367347 + 0.3918367347 + 0.4591836735x + x2 = 0 + 0.3918367347 Combine like terms: -0.3918367347 + 0.3918367347 = 0.0000000000 0.0000000000 + 0.4591836735x + x2 = 0 + 0.3918367347 0.4591836735x + x2 = 0 + 0.3918367347 Combine like terms: 0 + 0.3918367347 = 0.3918367347 0.4591836735x + x2 = 0.3918367347 The x term is 0.4591836735x. Take half its coefficient (0.2295918368). Square it (0.05271241153) and add it to both sides. Add '0.05271241153' to each side of the equation. 0.4591836735x + 0.05271241153 + x2 = 0.3918367347 + 0.05271241153 Reorder the terms: 0.05271241153 + 0.4591836735x + x2 = 0.3918367347 + 0.05271241153 Combine like terms: 0.3918367347 + 0.05271241153 = 0.44454914623 0.05271241153 + 0.4591836735x + x2 = 0.44454914623 Factor a perfect square on the left side: (x + 0.2295918368)(x + 0.2295918368) = 0.44454914623 Calculate the square root of the right side: 0.666745188 Break this problem into two subproblems by setting (x + 0.2295918368) equal to 0.666745188 and -0.666745188.Subproblem 1
x + 0.2295918368 = 0.666745188 Simplifying x + 0.2295918368 = 0.666745188 Reorder the terms: 0.2295918368 + x = 0.666745188 Solving 0.2295918368 + x = 0.666745188 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2295918368' to each side of the equation. 0.2295918368 + -0.2295918368 + x = 0.666745188 + -0.2295918368 Combine like terms: 0.2295918368 + -0.2295918368 = 0.0000000000 0.0000000000 + x = 0.666745188 + -0.2295918368 x = 0.666745188 + -0.2295918368 Combine like terms: 0.666745188 + -0.2295918368 = 0.4371533512 x = 0.4371533512 Simplifying x = 0.4371533512Subproblem 2
x + 0.2295918368 = -0.666745188 Simplifying x + 0.2295918368 = -0.666745188 Reorder the terms: 0.2295918368 + x = -0.666745188 Solving 0.2295918368 + x = -0.666745188 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2295918368' to each side of the equation. 0.2295918368 + -0.2295918368 + x = -0.666745188 + -0.2295918368 Combine like terms: 0.2295918368 + -0.2295918368 = 0.0000000000 0.0000000000 + x = -0.666745188 + -0.2295918368 x = -0.666745188 + -0.2295918368 Combine like terms: -0.666745188 + -0.2295918368 = -0.8963370248 x = -0.8963370248 Simplifying x = -0.8963370248Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4371533512, -0.8963370248}
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