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Simplifying 6 = 4x2 + -28x + 43 Reorder the terms: 6 = 43 + -28x + 4x2 Solving 6 = 43 + -28x + 4x2 Solving for variable 'x'. Combine like terms: 6 + -43 = -37 -37 + 28x + -4x2 = 43 + -28x + 4x2 + -43 + 28x + -4x2 Reorder the terms: -37 + 28x + -4x2 = 43 + -43 + -28x + 28x + 4x2 + -4x2 Combine like terms: 43 + -43 = 0 -37 + 28x + -4x2 = 0 + -28x + 28x + 4x2 + -4x2 -37 + 28x + -4x2 = -28x + 28x + 4x2 + -4x2 Combine like terms: -28x + 28x = 0 -37 + 28x + -4x2 = 0 + 4x2 + -4x2 -37 + 28x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -37 + 28x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 9.25 + -7x + x2 = 0 Move the constant term to the right: Add '-9.25' to each side of the equation. 9.25 + -7x + -9.25 + x2 = 0 + -9.25 Reorder the terms: 9.25 + -9.25 + -7x + x2 = 0 + -9.25 Combine like terms: 9.25 + -9.25 = 0.00 0.00 + -7x + x2 = 0 + -9.25 -7x + x2 = 0 + -9.25 Combine like terms: 0 + -9.25 = -9.25 -7x + x2 = -9.25 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = -9.25 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -9.25 + 12.25 Combine like terms: -9.25 + 12.25 = 3 12.25 + -7x + x2 = 3 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (x + -3.5) equal to 1.732050808 and -1.732050808.Subproblem 1
x + -3.5 = 1.732050808 Simplifying x + -3.5 = 1.732050808 Reorder the terms: -3.5 + x = 1.732050808 Solving -3.5 + x = 1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 1.732050808 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 1.732050808 + 3.5 x = 1.732050808 + 3.5 Combine like terms: 1.732050808 + 3.5 = 5.232050808 x = 5.232050808 Simplifying x = 5.232050808Subproblem 2
x + -3.5 = -1.732050808 Simplifying x + -3.5 = -1.732050808 Reorder the terms: -3.5 + x = -1.732050808 Solving -3.5 + x = -1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -1.732050808 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -1.732050808 + 3.5 x = -1.732050808 + 3.5 Combine like terms: -1.732050808 + 3.5 = 1.767949192 x = 1.767949192 Simplifying x = 1.767949192Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.232050808, 1.767949192}
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