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Simplifying 19.6212x2 + -145.692x + 125.94 = 0 Reorder the terms: 125.94 + -145.692x + 19.6212x2 = 0 Solving 125.94 + -145.692x + 19.6212x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 19.6212 the coefficient of the squared term: Divide each side by '19.6212'. 6.418567672 + -7.425233931x + x2 = 0 Move the constant term to the right: Add '-6.418567672' to each side of the equation. 6.418567672 + -7.425233931x + -6.418567672 + x2 = 0 + -6.418567672 Reorder the terms: 6.418567672 + -6.418567672 + -7.425233931x + x2 = 0 + -6.418567672 Combine like terms: 6.418567672 + -6.418567672 = 0.000000000 0.000000000 + -7.425233931x + x2 = 0 + -6.418567672 -7.425233931x + x2 = 0 + -6.418567672 Combine like terms: 0 + -6.418567672 = -6.418567672 -7.425233931x + x2 = -6.418567672 The x term is -7.425233931x. Take half its coefficient (-3.712616966). Square it (13.78352474) and add it to both sides. Add '13.78352474' to each side of the equation. -7.425233931x + 13.78352474 + x2 = -6.418567672 + 13.78352474 Reorder the terms: 13.78352474 + -7.425233931x + x2 = -6.418567672 + 13.78352474 Combine like terms: -6.418567672 + 13.78352474 = 7.364957068 13.78352474 + -7.425233931x + x2 = 7.364957068 Factor a perfect square on the left side: (x + -3.712616966)(x + -3.712616966) = 7.364957068 Calculate the square root of the right side: 2.713845439 Break this problem into two subproblems by setting (x + -3.712616966) equal to 2.713845439 and -2.713845439.Subproblem 1
x + -3.712616966 = 2.713845439 Simplifying x + -3.712616966 = 2.713845439 Reorder the terms: -3.712616966 + x = 2.713845439 Solving -3.712616966 + x = 2.713845439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.712616966' to each side of the equation. -3.712616966 + 3.712616966 + x = 2.713845439 + 3.712616966 Combine like terms: -3.712616966 + 3.712616966 = 0.000000000 0.000000000 + x = 2.713845439 + 3.712616966 x = 2.713845439 + 3.712616966 Combine like terms: 2.713845439 + 3.712616966 = 6.426462405 x = 6.426462405 Simplifying x = 6.426462405Subproblem 2
x + -3.712616966 = -2.713845439 Simplifying x + -3.712616966 = -2.713845439 Reorder the terms: -3.712616966 + x = -2.713845439 Solving -3.712616966 + x = -2.713845439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.712616966' to each side of the equation. -3.712616966 + 3.712616966 + x = -2.713845439 + 3.712616966 Combine like terms: -3.712616966 + 3.712616966 = 0.000000000 0.000000000 + x = -2.713845439 + 3.712616966 x = -2.713845439 + 3.712616966 Combine like terms: -2.713845439 + 3.712616966 = 0.998771527 x = 0.998771527 Simplifying x = 0.998771527Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.426462405, 0.998771527}
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