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Simplifying 6x2 + -240x + 900 = 0 Reorder the terms: 900 + -240x + 6x2 = 0 Solving 900 + -240x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(150 + -40x + x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(150 + -40x + x2)' equal to zero and attempt to solve: Simplifying 150 + -40x + x2 = 0 Solving 150 + -40x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-150' to each side of the equation. 150 + -40x + -150 + x2 = 0 + -150 Reorder the terms: 150 + -150 + -40x + x2 = 0 + -150 Combine like terms: 150 + -150 = 0 0 + -40x + x2 = 0 + -150 -40x + x2 = 0 + -150 Combine like terms: 0 + -150 = -150 -40x + x2 = -150 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 = -150 + 400 Reorder the terms: 400 + -40x + x2 = -150 + 400 Combine like terms: -150 + 400 = 250 400 + -40x + x2 = 250 Factor a perfect square on the left side: (x + -20)(x + -20) = 250 Calculate the square root of the right side: 15.811388301 Break this problem into two subproblems by setting (x + -20) equal to 15.811388301 and -15.811388301.Subproblem 1
x + -20 = 15.811388301 Simplifying x + -20 = 15.811388301 Reorder the terms: -20 + x = 15.811388301 Solving -20 + x = 15.811388301 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 = 15.811388301 + 20 Combine like terms: -20 + 20 = 0 0 + x = 15.811388301 + 20 x = 15.811388301 + 20 Combine like terms: 15.811388301 + 20 = 35.811388301 x = 35.811388301 Simplifying x = 35.811388301Subproblem 2
x + -20 = -15.811388301 Simplifying x + -20 = -15.811388301 Reorder the terms: -20 + x = -15.811388301 Solving -20 + x = -15.811388301 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 = -15.811388301 + 20 Combine like terms: -20 + 20 = 0 0 + x = -15.811388301 + 20 x = -15.811388301 + 20 Combine like terms: -15.811388301 + 20 = 4.188611699 x = 4.188611699 Simplifying x = 4.188611699Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.811388301, 4.188611699}Solution
x = {35.811388301, 4.188611699}
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