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Simplifying (200 + 50x)(4 + -1x) + 2400 + -400 + -200x + -1250 = 0 Multiply (200 + 50x) * (4 + -1x) (200(4 + -1x) + 50x * (4 + -1x)) + 2400 + -400 + -200x + -1250 = 0 ((4 * 200 + -1x * 200) + 50x * (4 + -1x)) + 2400 + -400 + -200x + -1250 = 0 ((800 + -200x) + 50x * (4 + -1x)) + 2400 + -400 + -200x + -1250 = 0 (800 + -200x + (4 * 50x + -1x * 50x)) + 2400 + -400 + -200x + -1250 = 0 (800 + -200x + (200x + -50x2)) + 2400 + -400 + -200x + -1250 = 0 Combine like terms: -200x + 200x = 0 (800 + 0 + -50x2) + 2400 + -400 + -200x + -1250 = 0 (800 + -50x2) + 2400 + -400 + -200x + -1250 = 0 Reorder the terms: 800 + 2400 + -400 + -1250 + -200x + -50x2 = 0 Combine like terms: 800 + 2400 = 3200 3200 + -400 + -1250 + -200x + -50x2 = 0 Combine like terms: 3200 + -400 = 2800 2800 + -1250 + -200x + -50x2 = 0 Combine like terms: 2800 + -1250 = 1550 1550 + -200x + -50x2 = 0 Solving 1550 + -200x + -50x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '50'. 50(31 + -4x + -1x2) = 0 Ignore the factor 50.Subproblem 1
Set the factor '(31 + -4x + -1x2)' equal to zero and attempt to solve: Simplifying 31 + -4x + -1x2 = 0 Solving 31 + -4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -31 + 4x + x2 = 0 Move the constant term to the right: Add '31' to each side of the equation. -31 + 4x + 31 + x2 = 0 + 31 Reorder the terms: -31 + 31 + 4x + x2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + 4x + x2 = 0 + 31 4x + x2 = 0 + 31 Combine like terms: 0 + 31 = 31 4x + x2 = 31 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 31 + 4 Reorder the terms: 4 + 4x + x2 = 31 + 4 Combine like terms: 31 + 4 = 35 4 + 4x + x2 = 35 Factor a perfect square on the left side: (x + 2)(x + 2) = 35 Calculate the square root of the right side: 5.916079783 Break this problem into two subproblems by setting (x + 2) equal to 5.916079783 and -5.916079783.Subproblem 1
x + 2 = 5.916079783 Simplifying x + 2 = 5.916079783 Reorder the terms: 2 + x = 5.916079783 Solving 2 + x = 5.916079783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 5.916079783 + -2 Combine like terms: 2 + -2 = 0 0 + x = 5.916079783 + -2 x = 5.916079783 + -2 Combine like terms: 5.916079783 + -2 = 3.916079783 x = 3.916079783 Simplifying x = 3.916079783Subproblem 2
x + 2 = -5.916079783 Simplifying x + 2 = -5.916079783 Reorder the terms: 2 + x = -5.916079783 Solving 2 + x = -5.916079783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -5.916079783 + -2 Combine like terms: 2 + -2 = 0 0 + x = -5.916079783 + -2 x = -5.916079783 + -2 Combine like terms: -5.916079783 + -2 = -7.916079783 x = -7.916079783 Simplifying x = -7.916079783Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.916079783, -7.916079783}Solution
x = {3.916079783, -7.916079783}
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