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Simplifying 47.56 + -43.3x + 9.40x2 = 0 Solving 47.56 + -43.3x + 9.40x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9.40 the coefficient of the squared term: Divide each side by '9.40'. 5.059574468 + -4.606382979x + x2 = 0 Move the constant term to the right: Add '-5.059574468' to each side of the equation. 5.059574468 + -4.606382979x + -5.059574468 + x2 = 0 + -5.059574468 Reorder the terms: 5.059574468 + -5.059574468 + -4.606382979x + x2 = 0 + -5.059574468 Combine like terms: 5.059574468 + -5.059574468 = 0.000000000 0.000000000 + -4.606382979x + x2 = 0 + -5.059574468 -4.606382979x + x2 = 0 + -5.059574468 Combine like terms: 0 + -5.059574468 = -5.059574468 -4.606382979x + x2 = -5.059574468 The x term is -4.606382979x. Take half its coefficient (-2.30319149). Square it (5.304691040) and add it to both sides. Add '5.304691040' to each side of the equation. -4.606382979x + 5.304691040 + x2 = -5.059574468 + 5.304691040 Reorder the terms: 5.304691040 + -4.606382979x + x2 = -5.059574468 + 5.304691040 Combine like terms: -5.059574468 + 5.304691040 = 0.245116572 5.304691040 + -4.606382979x + x2 = 0.245116572 Factor a perfect square on the left side: (x + -2.30319149)(x + -2.30319149) = 0.245116572 Calculate the square root of the right side: 0.495092488 Break this problem into two subproblems by setting (x + -2.30319149) equal to 0.495092488 and -0.495092488.Subproblem 1
x + -2.30319149 = 0.495092488 Simplifying x + -2.30319149 = 0.495092488 Reorder the terms: -2.30319149 + x = 0.495092488 Solving -2.30319149 + x = 0.495092488 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.30319149' to each side of the equation. -2.30319149 + 2.30319149 + x = 0.495092488 + 2.30319149 Combine like terms: -2.30319149 + 2.30319149 = 0.00000000 0.00000000 + x = 0.495092488 + 2.30319149 x = 0.495092488 + 2.30319149 Combine like terms: 0.495092488 + 2.30319149 = 2.798283978 x = 2.798283978 Simplifying x = 2.798283978Subproblem 2
x + -2.30319149 = -0.495092488 Simplifying x + -2.30319149 = -0.495092488 Reorder the terms: -2.30319149 + x = -0.495092488 Solving -2.30319149 + x = -0.495092488 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.30319149' to each side of the equation. -2.30319149 + 2.30319149 + x = -0.495092488 + 2.30319149 Combine like terms: -2.30319149 + 2.30319149 = 0.00000000 0.00000000 + x = -0.495092488 + 2.30319149 x = -0.495092488 + 2.30319149 Combine like terms: -0.495092488 + 2.30319149 = 1.808099002 x = 1.808099002 Simplifying x = 1.808099002Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.798283978, 1.808099002}
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