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Simplifying 4x2 + 28x + 37 = 0 Reorder the terms: 37 + 28x + 4x2 = 0 Solving 37 + 28x + 4x2 = 0 Solving for variable 'x'. 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 = -1.767949192 x = -1.767949192 Simplifying x = -1.767949192Subproblem 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 = -5.232050808 x = -5.232050808 Simplifying x = -5.232050808Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.767949192, -5.232050808}
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