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Simplifying -4.9x2 + 7.4x + 10.9 = 0 Reorder the terms: 10.9 + 7.4x + -4.9x2 = 0 Solving 10.9 + 7.4x + -4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -2.224489796 + -1.510204082x + x2 = 0 Move the constant term to the right: Add '2.224489796' to each side of the equation. -2.224489796 + -1.510204082x + 2.224489796 + x2 = 0 + 2.224489796 Reorder the terms: -2.224489796 + 2.224489796 + -1.510204082x + x2 = 0 + 2.224489796 Combine like terms: -2.224489796 + 2.224489796 = 0.000000000 0.000000000 + -1.510204082x + x2 = 0 + 2.224489796 -1.510204082x + x2 = 0 + 2.224489796 Combine like terms: 0 + 2.224489796 = 2.224489796 -1.510204082x + x2 = 2.224489796 The x term is -1.510204082x. Take half its coefficient (-0.755102041). Square it (0.5701790923) and add it to both sides. Add '0.5701790923' to each side of the equation. -1.510204082x + 0.5701790923 + x2 = 2.224489796 + 0.5701790923 Reorder the terms: 0.5701790923 + -1.510204082x + x2 = 2.224489796 + 0.5701790923 Combine like terms: 2.224489796 + 0.5701790923 = 2.7946688883 0.5701790923 + -1.510204082x + x2 = 2.7946688883 Factor a perfect square on the left side: (x + -0.755102041)(x + -0.755102041) = 2.7946688883 Calculate the square root of the right side: 1.67172632 Break this problem into two subproblems by setting (x + -0.755102041) equal to 1.67172632 and -1.67172632.Subproblem 1
x + -0.755102041 = 1.67172632 Simplifying x + -0.755102041 = 1.67172632 Reorder the terms: -0.755102041 + x = 1.67172632 Solving -0.755102041 + x = 1.67172632 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.755102041' to each side of the equation. -0.755102041 + 0.755102041 + x = 1.67172632 + 0.755102041 Combine like terms: -0.755102041 + 0.755102041 = 0.000000000 0.000000000 + x = 1.67172632 + 0.755102041 x = 1.67172632 + 0.755102041 Combine like terms: 1.67172632 + 0.755102041 = 2.426828361 x = 2.426828361 Simplifying x = 2.426828361Subproblem 2
x + -0.755102041 = -1.67172632 Simplifying x + -0.755102041 = -1.67172632 Reorder the terms: -0.755102041 + x = -1.67172632 Solving -0.755102041 + x = -1.67172632 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.755102041' to each side of the equation. -0.755102041 + 0.755102041 + x = -1.67172632 + 0.755102041 Combine like terms: -0.755102041 + 0.755102041 = 0.000000000 0.000000000 + x = -1.67172632 + 0.755102041 x = -1.67172632 + 0.755102041 Combine like terms: -1.67172632 + 0.755102041 = -0.916624279 x = -0.916624279 Simplifying x = -0.916624279Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.426828361, -0.916624279}
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