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Simplifying 0.35X2 + -0.753X + -21.6 = 0 Reorder the terms: -21.6 + -0.753X + 0.35X2 = 0 Solving -21.6 + -0.753X + 0.35X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 0.35 the coefficient of the squared term: Divide each side by '0.35'. -61.71428571 + -2.151428571X + X2 = 0 Move the constant term to the right: Add '61.71428571' to each side of the equation. -61.71428571 + -2.151428571X + 61.71428571 + X2 = 0 + 61.71428571 Reorder the terms: -61.71428571 + 61.71428571 + -2.151428571X + X2 = 0 + 61.71428571 Combine like terms: -61.71428571 + 61.71428571 = 0.00000000 0.00000000 + -2.151428571X + X2 = 0 + 61.71428571 -2.151428571X + X2 = 0 + 61.71428571 Combine like terms: 0 + 61.71428571 = 61.71428571 -2.151428571X + X2 = 61.71428571 The X term is -2.151428571X. Take half its coefficient (-1.075714286). Square it (1.157161225) and add it to both sides. Add '1.157161225' to each side of the equation. -2.151428571X + 1.157161225 + X2 = 61.71428571 + 1.157161225 Reorder the terms: 1.157161225 + -2.151428571X + X2 = 61.71428571 + 1.157161225 Combine like terms: 61.71428571 + 1.157161225 = 62.871446935 1.157161225 + -2.151428571X + X2 = 62.871446935 Factor a perfect square on the left side: (X + -1.075714286)(X + -1.075714286) = 62.871446935 Calculate the square root of the right side: 7.929151716 Break this problem into two subproblems by setting (X + -1.075714286) equal to 7.929151716 and -7.929151716.Subproblem 1
X + -1.075714286 = 7.929151716 Simplifying X + -1.075714286 = 7.929151716 Reorder the terms: -1.075714286 + X = 7.929151716 Solving -1.075714286 + X = 7.929151716 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1.075714286' to each side of the equation. -1.075714286 + 1.075714286 + X = 7.929151716 + 1.075714286 Combine like terms: -1.075714286 + 1.075714286 = 0.000000000 0.000000000 + X = 7.929151716 + 1.075714286 X = 7.929151716 + 1.075714286 Combine like terms: 7.929151716 + 1.075714286 = 9.004866002 X = 9.004866002 Simplifying X = 9.004866002Subproblem 2
X + -1.075714286 = -7.929151716 Simplifying X + -1.075714286 = -7.929151716 Reorder the terms: -1.075714286 + X = -7.929151716 Solving -1.075714286 + X = -7.929151716 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1.075714286' to each side of the equation. -1.075714286 + 1.075714286 + X = -7.929151716 + 1.075714286 Combine like terms: -1.075714286 + 1.075714286 = 0.000000000 0.000000000 + X = -7.929151716 + 1.075714286 X = -7.929151716 + 1.075714286 Combine like terms: -7.929151716 + 1.075714286 = -6.85343743 X = -6.85343743 Simplifying X = -6.85343743Solution
The solution to the problem is based on the solutions from the subproblems. X = {9.004866002, -6.85343743}
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