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Simplifying 56 = (x + 3 + -4)(x + -4) Reorder the terms: 56 = (3 + -4 + x)(x + -4) Combine like terms: 3 + -4 = -1 56 = (-1 + x)(x + -4) Reorder the terms: 56 = (-1 + x)(-4 + x) Multiply (-1 + x) * (-4 + x) 56 = (-1(-4 + x) + x(-4 + x)) 56 = ((-4 * -1 + x * -1) + x(-4 + x)) 56 = ((4 + -1x) + x(-4 + x)) 56 = (4 + -1x + (-4 * x + x * x)) 56 = (4 + -1x + (-4x + x2)) Combine like terms: -1x + -4x = -5x 56 = (4 + -5x + x2) Solving 56 = 4 + -5x + x2 Solving for variable 'x'. Combine like terms: 56 + -4 = 52 52 + 5x + -1x2 = 4 + -5x + x2 + -4 + 5x + -1x2 Reorder the terms: 52 + 5x + -1x2 = 4 + -4 + -5x + 5x + x2 + -1x2 Combine like terms: 4 + -4 = 0 52 + 5x + -1x2 = 0 + -5x + 5x + x2 + -1x2 52 + 5x + -1x2 = -5x + 5x + x2 + -1x2 Combine like terms: -5x + 5x = 0 52 + 5x + -1x2 = 0 + x2 + -1x2 52 + 5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 52 + 5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -52 + -5x + x2 = 0 Move the constant term to the right: Add '52' to each side of the equation. -52 + -5x + 52 + x2 = 0 + 52 Reorder the terms: -52 + 52 + -5x + x2 = 0 + 52 Combine like terms: -52 + 52 = 0 0 + -5x + x2 = 0 + 52 -5x + x2 = 0 + 52 Combine like terms: 0 + 52 = 52 -5x + x2 = 52 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 52 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 52 + 6.25 Combine like terms: 52 + 6.25 = 58.25 6.25 + -5x + x2 = 58.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 58.25 Calculate the square root of the right side: 7.632168761 Break this problem into two subproblems by setting (x + -2.5) equal to 7.632168761 and -7.632168761.Subproblem 1
x + -2.5 = 7.632168761 Simplifying x + -2.5 = 7.632168761 Reorder the terms: -2.5 + x = 7.632168761 Solving -2.5 + x = 7.632168761 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 7.632168761 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 7.632168761 + 2.5 x = 7.632168761 + 2.5 Combine like terms: 7.632168761 + 2.5 = 10.132168761 x = 10.132168761 Simplifying x = 10.132168761Subproblem 2
x + -2.5 = -7.632168761 Simplifying x + -2.5 = -7.632168761 Reorder the terms: -2.5 + x = -7.632168761 Solving -2.5 + x = -7.632168761 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -7.632168761 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -7.632168761 + 2.5 x = -7.632168761 + 2.5 Combine like terms: -7.632168761 + 2.5 = -5.132168761 x = -5.132168761 Simplifying x = -5.132168761Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.132168761, -5.132168761}
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