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Simplifying (x)(28 + 4x) = 73 (28 * x + 4x * x) = 73 (28x + 4x2) = 73 Solving 28x + 4x2 = 73 Solving for variable 'x'. Reorder the terms: -73 + 28x + 4x2 = 73 + -73 Combine like terms: 73 + -73 = 0 -73 + 28x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -18.25 + 7x + x2 = 0 Move the constant term to the right: Add '18.25' to each side of the equation. -18.25 + 7x + 18.25 + x2 = 0 + 18.25 Reorder the terms: -18.25 + 18.25 + 7x + x2 = 0 + 18.25 Combine like terms: -18.25 + 18.25 = 0.00 0.00 + 7x + x2 = 0 + 18.25 7x + x2 = 0 + 18.25 Combine like terms: 0 + 18.25 = 18.25 7x + x2 = 18.25 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 = 18.25 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 18.25 + 12.25 Combine like terms: 18.25 + 12.25 = 30.5 12.25 + 7x + x2 = 30.5 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 30.5 Calculate the square root of the right side: 5.522680509 Break this problem into two subproblems by setting (x + 3.5) equal to 5.522680509 and -5.522680509.Subproblem 1
x + 3.5 = 5.522680509 Simplifying x + 3.5 = 5.522680509 Reorder the terms: 3.5 + x = 5.522680509 Solving 3.5 + x = 5.522680509 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 = 5.522680509 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 5.522680509 + -3.5 x = 5.522680509 + -3.5 Combine like terms: 5.522680509 + -3.5 = 2.022680509 x = 2.022680509 Simplifying x = 2.022680509Subproblem 2
x + 3.5 = -5.522680509 Simplifying x + 3.5 = -5.522680509 Reorder the terms: 3.5 + x = -5.522680509 Solving 3.5 + x = -5.522680509 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 = -5.522680509 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -5.522680509 + -3.5 x = -5.522680509 + -3.5 Combine like terms: -5.522680509 + -3.5 = -9.022680509 x = -9.022680509 Simplifying x = -9.022680509Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.022680509, -9.022680509}
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