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Simplifying 2x2 + -28x + 9 = 0 Reorder the terms: 9 + -28x + 2x2 = 0 Solving 9 + -28x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4.5 + -14x + x2 = 0 Move the constant term to the right: Add '-4.5' to each side of the equation. 4.5 + -14x + -4.5 + x2 = 0 + -4.5 Reorder the terms: 4.5 + -4.5 + -14x + x2 = 0 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + -14x + x2 = 0 + -4.5 -14x + x2 = 0 + -4.5 Combine like terms: 0 + -4.5 = -4.5 -14x + x2 = -4.5 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = -4.5 + 49 Reorder the terms: 49 + -14x + x2 = -4.5 + 49 Combine like terms: -4.5 + 49 = 44.5 49 + -14x + x2 = 44.5 Factor a perfect square on the left side: (x + -7)(x + -7) = 44.5 Calculate the square root of the right side: 6.670832032 Break this problem into two subproblems by setting (x + -7) equal to 6.670832032 and -6.670832032.Subproblem 1
x + -7 = 6.670832032 Simplifying x + -7 = 6.670832032 Reorder the terms: -7 + x = 6.670832032 Solving -7 + x = 6.670832032 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 6.670832032 + 7 Combine like terms: -7 + 7 = 0 0 + x = 6.670832032 + 7 x = 6.670832032 + 7 Combine like terms: 6.670832032 + 7 = 13.670832032 x = 13.670832032 Simplifying x = 13.670832032Subproblem 2
x + -7 = -6.670832032 Simplifying x + -7 = -6.670832032 Reorder the terms: -7 + x = -6.670832032 Solving -7 + x = -6.670832032 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -6.670832032 + 7 Combine like terms: -7 + 7 = 0 0 + x = -6.670832032 + 7 x = -6.670832032 + 7 Combine like terms: -6.670832032 + 7 = 0.329167968 x = 0.329167968 Simplifying x = 0.329167968Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.670832032, 0.329167968}
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