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Simplifying 4x(x + -7) = 11 Reorder the terms: 4x(-7 + x) = 11 (-7 * 4x + x * 4x) = 11 (-28x + 4x2) = 11 Solving -28x + 4x2 = 11 Solving for variable 'x'. Reorder the terms: -11 + -28x + 4x2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + -28x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.75 + -7x + x2 = 0 Move the constant term to the right: Add '2.75' to each side of the equation. -2.75 + -7x + 2.75 + x2 = 0 + 2.75 Reorder the terms: -2.75 + 2.75 + -7x + x2 = 0 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + -7x + x2 = 0 + 2.75 -7x + x2 = 0 + 2.75 Combine like terms: 0 + 2.75 = 2.75 -7x + x2 = 2.75 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 = 2.75 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 2.75 + 12.25 Combine like terms: 2.75 + 12.25 = 15 12.25 + -7x + x2 = 15 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (x + -3.5) equal to 3.872983346 and -3.872983346.Subproblem 1
x + -3.5 = 3.872983346 Simplifying x + -3.5 = 3.872983346 Reorder the terms: -3.5 + x = 3.872983346 Solving -3.5 + x = 3.872983346 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 = 3.872983346 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 3.872983346 + 3.5 x = 3.872983346 + 3.5 Combine like terms: 3.872983346 + 3.5 = 7.372983346 x = 7.372983346 Simplifying x = 7.372983346Subproblem 2
x + -3.5 = -3.872983346 Simplifying x + -3.5 = -3.872983346 Reorder the terms: -3.5 + x = -3.872983346 Solving -3.5 + x = -3.872983346 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 = -3.872983346 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -3.872983346 + 3.5 x = -3.872983346 + 3.5 Combine like terms: -3.872983346 + 3.5 = -0.372983346 x = -0.372983346 Simplifying x = -0.372983346Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.372983346, -0.372983346}
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