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Simplifying 4x(x + 7) = -23 Reorder the terms: 4x(7 + x) = -23 (7 * 4x + x * 4x) = -23 (28x + 4x2) = -23 Solving 28x + 4x2 = -23 Solving for variable 'x'. Reorder the terms: 23 + 28x + 4x2 = -23 + 23 Combine like terms: -23 + 23 = 0 23 + 28x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 5.75 + 7x + x2 = 0 Move the constant term to the right: Add '-5.75' to each side of the equation. 5.75 + 7x + -5.75 + x2 = 0 + -5.75 Reorder the terms: 5.75 + -5.75 + 7x + x2 = 0 + -5.75 Combine like terms: 5.75 + -5.75 = 0.00 0.00 + 7x + x2 = 0 + -5.75 7x + x2 = 0 + -5.75 Combine like terms: 0 + -5.75 = -5.75 7x + x2 = -5.75 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 = -5.75 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -5.75 + 12.25 Combine like terms: -5.75 + 12.25 = 6.5 12.25 + 7x + x2 = 6.5 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 6.5 Calculate the square root of the right side: 2.549509757 Break this problem into two subproblems by setting (x + 3.5) equal to 2.549509757 and -2.549509757.Subproblem 1
x + 3.5 = 2.549509757 Simplifying x + 3.5 = 2.549509757 Reorder the terms: 3.5 + x = 2.549509757 Solving 3.5 + x = 2.549509757 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 = 2.549509757 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 2.549509757 + -3.5 x = 2.549509757 + -3.5 Combine like terms: 2.549509757 + -3.5 = -0.950490243 x = -0.950490243 Simplifying x = -0.950490243Subproblem 2
x + 3.5 = -2.549509757 Simplifying x + 3.5 = -2.549509757 Reorder the terms: 3.5 + x = -2.549509757 Solving 3.5 + x = -2.549509757 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 = -2.549509757 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -2.549509757 + -3.5 x = -2.549509757 + -3.5 Combine like terms: -2.549509757 + -3.5 = -6.049509757 x = -6.049509757 Simplifying x = -6.049509757Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.950490243, -6.049509757}
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