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Simplifying 0.7x2 + -12x + 44 = 0 Reorder the terms: 44 + -12x + 0.7x2 = 0 Solving 44 + -12x + 0.7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.7 the coefficient of the squared term: Divide each side by '0.7'. 62.85714286 + -17.14285714x + x2 = 0 Move the constant term to the right: Add '-62.85714286' to each side of the equation. 62.85714286 + -17.14285714x + -62.85714286 + x2 = 0 + -62.85714286 Reorder the terms: 62.85714286 + -62.85714286 + -17.14285714x + x2 = 0 + -62.85714286 Combine like terms: 62.85714286 + -62.85714286 = 0.00000000 0.00000000 + -17.14285714x + x2 = 0 + -62.85714286 -17.14285714x + x2 = 0 + -62.85714286 Combine like terms: 0 + -62.85714286 = -62.85714286 -17.14285714x + x2 = -62.85714286 The x term is -17.14285714x. Take half its coefficient (-8.57142857). Square it (73.46938773) and add it to both sides. Add '73.46938773' to each side of the equation. -17.14285714x + 73.46938773 + x2 = -62.85714286 + 73.46938773 Reorder the terms: 73.46938773 + -17.14285714x + x2 = -62.85714286 + 73.46938773 Combine like terms: -62.85714286 + 73.46938773 = 10.61224487 73.46938773 + -17.14285714x + x2 = 10.61224487 Factor a perfect square on the left side: (x + -8.57142857)(x + -8.57142857) = 10.61224487 Calculate the square root of the right side: 3.257644067 Break this problem into two subproblems by setting (x + -8.57142857) equal to 3.257644067 and -3.257644067.Subproblem 1
x + -8.57142857 = 3.257644067 Simplifying x + -8.57142857 = 3.257644067 Reorder the terms: -8.57142857 + x = 3.257644067 Solving -8.57142857 + x = 3.257644067 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.57142857' to each side of the equation. -8.57142857 + 8.57142857 + x = 3.257644067 + 8.57142857 Combine like terms: -8.57142857 + 8.57142857 = 0.00000000 0.00000000 + x = 3.257644067 + 8.57142857 x = 3.257644067 + 8.57142857 Combine like terms: 3.257644067 + 8.57142857 = 11.829072637 x = 11.829072637 Simplifying x = 11.829072637Subproblem 2
x + -8.57142857 = -3.257644067 Simplifying x + -8.57142857 = -3.257644067 Reorder the terms: -8.57142857 + x = -3.257644067 Solving -8.57142857 + x = -3.257644067 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.57142857' to each side of the equation. -8.57142857 + 8.57142857 + x = -3.257644067 + 8.57142857 Combine like terms: -8.57142857 + 8.57142857 = 0.00000000 0.00000000 + x = -3.257644067 + 8.57142857 x = -3.257644067 + 8.57142857 Combine like terms: -3.257644067 + 8.57142857 = 5.313784503 x = 5.313784503 Simplifying x = 5.313784503Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.829072637, 5.313784503}
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