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Simplifying (x + -7)(x + -4) = 80 Reorder the terms: (-7 + x)(x + -4) = 80 Reorder the terms: (-7 + x)(-4 + x) = 80 Multiply (-7 + x) * (-4 + x) (-7(-4 + x) + x(-4 + x)) = 80 ((-4 * -7 + x * -7) + x(-4 + x)) = 80 ((28 + -7x) + x(-4 + x)) = 80 (28 + -7x + (-4 * x + x * x)) = 80 (28 + -7x + (-4x + x2)) = 80 Combine like terms: -7x + -4x = -11x (28 + -11x + x2) = 80 Solving 28 + -11x + x2 = 80 Solving for variable 'x'. Reorder the terms: 28 + -80 + -11x + x2 = 80 + -80 Combine like terms: 28 + -80 = -52 -52 + -11x + x2 = 80 + -80 Combine like terms: 80 + -80 = 0 -52 + -11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '52' to each side of the equation. -52 + -11x + 52 + x2 = 0 + 52 Reorder the terms: -52 + 52 + -11x + x2 = 0 + 52 Combine like terms: -52 + 52 = 0 0 + -11x + x2 = 0 + 52 -11x + x2 = 0 + 52 Combine like terms: 0 + 52 = 52 -11x + x2 = 52 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = 52 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 52 + 30.25 Combine like terms: 52 + 30.25 = 82.25 30.25 + -11x + x2 = 82.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 82.25 Calculate the square root of the right side: 9.069178574 Break this problem into two subproblems by setting (x + -5.5) equal to 9.069178574 and -9.069178574.Subproblem 1
x + -5.5 = 9.069178574 Simplifying x + -5.5 = 9.069178574 Reorder the terms: -5.5 + x = 9.069178574 Solving -5.5 + x = 9.069178574 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 9.069178574 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 9.069178574 + 5.5 x = 9.069178574 + 5.5 Combine like terms: 9.069178574 + 5.5 = 14.569178574 x = 14.569178574 Simplifying x = 14.569178574Subproblem 2
x + -5.5 = -9.069178574 Simplifying x + -5.5 = -9.069178574 Reorder the terms: -5.5 + x = -9.069178574 Solving -5.5 + x = -9.069178574 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -9.069178574 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -9.069178574 + 5.5 x = -9.069178574 + 5.5 Combine like terms: -9.069178574 + 5.5 = -3.569178574 x = -3.569178574 Simplifying x = -3.569178574Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.569178574, -3.569178574}
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