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Simplifying 160x + 4x2 = 200 Solving 160x + 4x2 = 200 Solving for variable 'x'. Reorder the terms: -200 + 160x + 4x2 = 200 + -200 Combine like terms: 200 + -200 = 0 -200 + 160x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-50 + 40x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-50 + 40x + x2)' equal to zero and attempt to solve: Simplifying -50 + 40x + x2 = 0 Solving -50 + 40x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + 40x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + 40x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 40x + x2 = 0 + 50 40x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 40x + x2 = 50 The x term is 40x. Take half its coefficient (20). Square it (400) and add it to both sides. Add '400' to each side of the equation. 40x + 400 + x2 = 50 + 400 Reorder the terms: 400 + 40x + x2 = 50 + 400 Combine like terms: 50 + 400 = 450 400 + 40x + x2 = 450 Factor a perfect square on the left side: (x + 20)(x + 20) = 450 Calculate the square root of the right side: 21.213203436 Break this problem into two subproblems by setting (x + 20) equal to 21.213203436 and -21.213203436.Subproblem 1
x + 20 = 21.213203436 Simplifying x + 20 = 21.213203436 Reorder the terms: 20 + x = 21.213203436 Solving 20 + x = 21.213203436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = 21.213203436 + -20 Combine like terms: 20 + -20 = 0 0 + x = 21.213203436 + -20 x = 21.213203436 + -20 Combine like terms: 21.213203436 + -20 = 1.213203436 x = 1.213203436 Simplifying x = 1.213203436Subproblem 2
x + 20 = -21.213203436 Simplifying x + 20 = -21.213203436 Reorder the terms: 20 + x = -21.213203436 Solving 20 + x = -21.213203436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = -21.213203436 + -20 Combine like terms: 20 + -20 = 0 0 + x = -21.213203436 + -20 x = -21.213203436 + -20 Combine like terms: -21.213203436 + -20 = -41.213203436 x = -41.213203436 Simplifying x = -41.213203436Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.213203436, -41.213203436}Solution
x = {1.213203436, -41.213203436}
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