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Simplifying 500 = (x + -10)(x + 5) Reorder the terms: 500 = (-10 + x)(x + 5) Reorder the terms: 500 = (-10 + x)(5 + x) Multiply (-10 + x) * (5 + x) 500 = (-10(5 + x) + x(5 + x)) 500 = ((5 * -10 + x * -10) + x(5 + x)) 500 = ((-50 + -10x) + x(5 + x)) 500 = (-50 + -10x + (5 * x + x * x)) 500 = (-50 + -10x + (5x + x2)) Combine like terms: -10x + 5x = -5x 500 = (-50 + -5x + x2) Solving 500 = -50 + -5x + x2 Solving for variable 'x'. Combine like terms: 500 + 50 = 550 550 + 5x + -1x2 = -50 + -5x + x2 + 50 + 5x + -1x2 Reorder the terms: 550 + 5x + -1x2 = -50 + 50 + -5x + 5x + x2 + -1x2 Combine like terms: -50 + 50 = 0 550 + 5x + -1x2 = 0 + -5x + 5x + x2 + -1x2 550 + 5x + -1x2 = -5x + 5x + x2 + -1x2 Combine like terms: -5x + 5x = 0 550 + 5x + -1x2 = 0 + x2 + -1x2 550 + 5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 550 + 5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -550 + -5x + x2 = 0 Move the constant term to the right: Add '550' to each side of the equation. -550 + -5x + 550 + x2 = 0 + 550 Reorder the terms: -550 + 550 + -5x + x2 = 0 + 550 Combine like terms: -550 + 550 = 0 0 + -5x + x2 = 0 + 550 -5x + x2 = 0 + 550 Combine like terms: 0 + 550 = 550 -5x + x2 = 550 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 = 550 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 550 + 6.25 Combine like terms: 550 + 6.25 = 556.25 6.25 + -5x + x2 = 556.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 556.25 Calculate the square root of the right side: 23.58495283 Break this problem into two subproblems by setting (x + -2.5) equal to 23.58495283 and -23.58495283.Subproblem 1
x + -2.5 = 23.58495283 Simplifying x + -2.5 = 23.58495283 Reorder the terms: -2.5 + x = 23.58495283 Solving -2.5 + x = 23.58495283 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 = 23.58495283 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 23.58495283 + 2.5 x = 23.58495283 + 2.5 Combine like terms: 23.58495283 + 2.5 = 26.08495283 x = 26.08495283 Simplifying x = 26.08495283Subproblem 2
x + -2.5 = -23.58495283 Simplifying x + -2.5 = -23.58495283 Reorder the terms: -2.5 + x = -23.58495283 Solving -2.5 + x = -23.58495283 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 = -23.58495283 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -23.58495283 + 2.5 x = -23.58495283 + 2.5 Combine like terms: -23.58495283 + 2.5 = -21.08495283 x = -21.08495283 Simplifying x = -21.08495283Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.08495283, -21.08495283}
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