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Simplifying 2400 + 160x + -4x2 = 0 Solving 2400 + 160x + -4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(600 + 40x + -1x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(600 + 40x + -1x2)' equal to zero and attempt to solve: Simplifying 600 + 40x + -1x2 = 0 Solving 600 + 40x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -600 + -40x + x2 = 0 Move the constant term to the right: Add '600' to each side of the equation. -600 + -40x + 600 + x2 = 0 + 600 Reorder the terms: -600 + 600 + -40x + x2 = 0 + 600 Combine like terms: -600 + 600 = 0 0 + -40x + x2 = 0 + 600 -40x + x2 = 0 + 600 Combine like terms: 0 + 600 = 600 -40x + x2 = 600 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 = 600 + 400 Reorder the terms: 400 + -40x + x2 = 600 + 400 Combine like terms: 600 + 400 = 1000 400 + -40x + x2 = 1000 Factor a perfect square on the left side: (x + -20)(x + -20) = 1000 Calculate the square root of the right side: 31.622776602 Break this problem into two subproblems by setting (x + -20) equal to 31.622776602 and -31.622776602.Subproblem 1
x + -20 = 31.622776602 Simplifying x + -20 = 31.622776602 Reorder the terms: -20 + x = 31.622776602 Solving -20 + x = 31.622776602 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 = 31.622776602 + 20 Combine like terms: -20 + 20 = 0 0 + x = 31.622776602 + 20 x = 31.622776602 + 20 Combine like terms: 31.622776602 + 20 = 51.622776602 x = 51.622776602 Simplifying x = 51.622776602Subproblem 2
x + -20 = -31.622776602 Simplifying x + -20 = -31.622776602 Reorder the terms: -20 + x = -31.622776602 Solving -20 + x = -31.622776602 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 = -31.622776602 + 20 Combine like terms: -20 + 20 = 0 0 + x = -31.622776602 + 20 x = -31.622776602 + 20 Combine like terms: -31.622776602 + 20 = -11.622776602 x = -11.622776602 Simplifying x = -11.622776602Solution
The solution to the problem is based on the solutions from the subproblems. x = {51.622776602, -11.622776602}Solution
x = {51.622776602, -11.622776602}
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