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Simplifying -4.905x2 + 1.6x + 2.64 = 0 Reorder the terms: 2.64 + 1.6x + -4.905x2 = 0 Solving 2.64 + 1.6x + -4.905x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4.905 the coefficient of the squared term: Divide each side by '-4.905'. -0.5382262997 + -0.3261977574x + x2 = 0 Move the constant term to the right: Add '0.5382262997' to each side of the equation. -0.5382262997 + -0.3261977574x + 0.5382262997 + x2 = 0 + 0.5382262997 Reorder the terms: -0.5382262997 + 0.5382262997 + -0.3261977574x + x2 = 0 + 0.5382262997 Combine like terms: -0.5382262997 + 0.5382262997 = 0.0000000000 0.0000000000 + -0.3261977574x + x2 = 0 + 0.5382262997 -0.3261977574x + x2 = 0 + 0.5382262997 Combine like terms: 0 + 0.5382262997 = 0.5382262997 -0.3261977574x + x2 = 0.5382262997 The x term is -0.3261977574x. Take half its coefficient (-0.1630988787). Square it (0.02660124423) and add it to both sides. Add '0.02660124423' to each side of the equation. -0.3261977574x + 0.02660124423 + x2 = 0.5382262997 + 0.02660124423 Reorder the terms: 0.02660124423 + -0.3261977574x + x2 = 0.5382262997 + 0.02660124423 Combine like terms: 0.5382262997 + 0.02660124423 = 0.56482754393 0.02660124423 + -0.3261977574x + x2 = 0.56482754393 Factor a perfect square on the left side: (x + -0.1630988787)(x + -0.1630988787) = 0.56482754393 Calculate the square root of the right side: 0.751550094 Break this problem into two subproblems by setting (x + -0.1630988787) equal to 0.751550094 and -0.751550094.Subproblem 1
x + -0.1630988787 = 0.751550094 Simplifying x + -0.1630988787 = 0.751550094 Reorder the terms: -0.1630988787 + x = 0.751550094 Solving -0.1630988787 + x = 0.751550094 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1630988787' to each side of the equation. -0.1630988787 + 0.1630988787 + x = 0.751550094 + 0.1630988787 Combine like terms: -0.1630988787 + 0.1630988787 = 0.0000000000 0.0000000000 + x = 0.751550094 + 0.1630988787 x = 0.751550094 + 0.1630988787 Combine like terms: 0.751550094 + 0.1630988787 = 0.9146489727 x = 0.9146489727 Simplifying x = 0.9146489727Subproblem 2
x + -0.1630988787 = -0.751550094 Simplifying x + -0.1630988787 = -0.751550094 Reorder the terms: -0.1630988787 + x = -0.751550094 Solving -0.1630988787 + x = -0.751550094 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1630988787' to each side of the equation. -0.1630988787 + 0.1630988787 + x = -0.751550094 + 0.1630988787 Combine like terms: -0.1630988787 + 0.1630988787 = 0.0000000000 0.0000000000 + x = -0.751550094 + 0.1630988787 x = -0.751550094 + 0.1630988787 Combine like terms: -0.751550094 + 0.1630988787 = -0.5884512153 x = -0.5884512153 Simplifying x = -0.5884512153Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9146489727, -0.5884512153}
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