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Simplifying 4x = (x + -4)(x + 5) Reorder the terms: 4x = (-4 + x)(x + 5) Reorder the terms: 4x = (-4 + x)(5 + x) Multiply (-4 + x) * (5 + x) 4x = (-4(5 + x) + x(5 + x)) 4x = ((5 * -4 + x * -4) + x(5 + x)) 4x = ((-20 + -4x) + x(5 + x)) 4x = (-20 + -4x + (5 * x + x * x)) 4x = (-20 + -4x + (5x + x2)) Combine like terms: -4x + 5x = 1x 4x = (-20 + 1x + x2) Solving 4x = -20 + 1x + x2 Solving for variable 'x'. Reorder the terms: 20 + 4x + -1x + -1x2 = -20 + 1x + x2 + 20 + -1x + -1x2 Combine like terms: 4x + -1x = 3x 20 + 3x + -1x2 = -20 + 1x + x2 + 20 + -1x + -1x2 Reorder the terms: 20 + 3x + -1x2 = -20 + 20 + 1x + -1x + x2 + -1x2 Combine like terms: -20 + 20 = 0 20 + 3x + -1x2 = 0 + 1x + -1x + x2 + -1x2 20 + 3x + -1x2 = 1x + -1x + x2 + -1x2 Combine like terms: 1x + -1x = 0 20 + 3x + -1x2 = 0 + x2 + -1x2 20 + 3x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 20 + 3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -20 + -3x + x2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + -3x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + -3x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -3x + x2 = 0 + 20 -3x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 -3x + x2 = 20 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 20 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 20 + 2.25 Combine like terms: 20 + 2.25 = 22.25 2.25 + -3x + x2 = 22.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 22.25 Calculate the square root of the right side: 4.716990566 Break this problem into two subproblems by setting (x + -1.5) equal to 4.716990566 and -4.716990566.Subproblem 1
x + -1.5 = 4.716990566 Simplifying x + -1.5 = 4.716990566 Reorder the terms: -1.5 + x = 4.716990566 Solving -1.5 + x = 4.716990566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 4.716990566 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 4.716990566 + 1.5 x = 4.716990566 + 1.5 Combine like terms: 4.716990566 + 1.5 = 6.216990566 x = 6.216990566 Simplifying x = 6.216990566Subproblem 2
x + -1.5 = -4.716990566 Simplifying x + -1.5 = -4.716990566 Reorder the terms: -1.5 + x = -4.716990566 Solving -1.5 + x = -4.716990566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -4.716990566 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -4.716990566 + 1.5 x = -4.716990566 + 1.5 Combine like terms: -4.716990566 + 1.5 = -3.216990566 x = -3.216990566 Simplifying x = -3.216990566Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.216990566, -3.216990566}
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