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Simplifying 4x2 + 28x = -47 Reorder the terms: 28x + 4x2 = -47 Solving 28x + 4x2 = -47 Solving for variable 'x'. Reorder the terms: 47 + 28x + 4x2 = -47 + 47 Combine like terms: -47 + 47 = 0 47 + 28x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 11.75 + 7x + x2 = 0 Move the constant term to the right: Add '-11.75' to each side of the equation. 11.75 + 7x + -11.75 + x2 = 0 + -11.75 Reorder the terms: 11.75 + -11.75 + 7x + x2 = 0 + -11.75 Combine like terms: 11.75 + -11.75 = 0.00 0.00 + 7x + x2 = 0 + -11.75 7x + x2 = 0 + -11.75 Combine like terms: 0 + -11.75 = -11.75 7x + x2 = -11.75 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 = -11.75 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -11.75 + 12.25 Combine like terms: -11.75 + 12.25 = 0.5 12.25 + 7x + x2 = 0.5 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 0.5 Calculate the square root of the right side: 0.707106781 Break this problem into two subproblems by setting (x + 3.5) equal to 0.707106781 and -0.707106781.Subproblem 1
x + 3.5 = 0.707106781 Simplifying x + 3.5 = 0.707106781 Reorder the terms: 3.5 + x = 0.707106781 Solving 3.5 + x = 0.707106781 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 = 0.707106781 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 0.707106781 + -3.5 x = 0.707106781 + -3.5 Combine like terms: 0.707106781 + -3.5 = -2.792893219 x = -2.792893219 Simplifying x = -2.792893219Subproblem 2
x + 3.5 = -0.707106781 Simplifying x + 3.5 = -0.707106781 Reorder the terms: 3.5 + x = -0.707106781 Solving 3.5 + x = -0.707106781 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 = -0.707106781 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -0.707106781 + -3.5 x = -0.707106781 + -3.5 Combine like terms: -0.707106781 + -3.5 = -4.207106781 x = -4.207106781 Simplifying x = -4.207106781Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.792893219, -4.207106781}
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