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Simplifying 4x2 + 28x + -69 = 0 Reorder the terms: -69 + 28x + 4x2 = 0 Solving -69 + 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'. -17.25 + 7x + x2 = 0 Move the constant term to the right: Add '17.25' to each side of the equation. -17.25 + 7x + 17.25 + x2 = 0 + 17.25 Reorder the terms: -17.25 + 17.25 + 7x + x2 = 0 + 17.25 Combine like terms: -17.25 + 17.25 = 0.00 0.00 + 7x + x2 = 0 + 17.25 7x + x2 = 0 + 17.25 Combine like terms: 0 + 17.25 = 17.25 7x + x2 = 17.25 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 = 17.25 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 17.25 + 12.25 Combine like terms: 17.25 + 12.25 = 29.5 12.25 + 7x + x2 = 29.5 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 29.5 Calculate the square root of the right side: 5.431390246 Break this problem into two subproblems by setting (x + 3.5) equal to 5.431390246 and -5.431390246.Subproblem 1
x + 3.5 = 5.431390246 Simplifying x + 3.5 = 5.431390246 Reorder the terms: 3.5 + x = 5.431390246 Solving 3.5 + x = 5.431390246 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 = 5.431390246 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 5.431390246 + -3.5 x = 5.431390246 + -3.5 Combine like terms: 5.431390246 + -3.5 = 1.931390246 x = 1.931390246 Simplifying x = 1.931390246Subproblem 2
x + 3.5 = -5.431390246 Simplifying x + 3.5 = -5.431390246 Reorder the terms: 3.5 + x = -5.431390246 Solving 3.5 + x = -5.431390246 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 = -5.431390246 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -5.431390246 + -3.5 x = -5.431390246 + -3.5 Combine like terms: -5.431390246 + -3.5 = -8.931390246 x = -8.931390246 Simplifying x = -8.931390246Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.931390246, -8.931390246}
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