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Simplifying 3(x2 + -640x + -45) = 0 Reorder the terms: 3(-45 + -640x + x2) = 0 (-45 * 3 + -640x * 3 + x2 * 3) = 0 (-135 + -1920x + 3x2) = 0 Solving -135 + -1920x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-45 + -640x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-45 + -640x + x2)' equal to zero and attempt to solve: Simplifying -45 + -640x + x2 = 0 Solving -45 + -640x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + -640x + 45 + x2 = 0 + 45 Reorder the terms: -45 + 45 + -640x + x2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + -640x + x2 = 0 + 45 -640x + x2 = 0 + 45 Combine like terms: 0 + 45 = 45 -640x + x2 = 45 The x term is -640x. Take half its coefficient (-320). Square it (102400) and add it to both sides. Add '102400' to each side of the equation. -640x + 102400 + x2 = 45 + 102400 Reorder the terms: 102400 + -640x + x2 = 45 + 102400 Combine like terms: 45 + 102400 = 102445 102400 + -640x + x2 = 102445 Factor a perfect square on the left side: (x + -320)(x + -320) = 102445 Calculate the square root of the right side: 320.070304777 Break this problem into two subproblems by setting (x + -320) equal to 320.070304777 and -320.070304777.Subproblem 1
x + -320 = 320.070304777 Simplifying x + -320 = 320.070304777 Reorder the terms: -320 + x = 320.070304777 Solving -320 + x = 320.070304777 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '320' to each side of the equation. -320 + 320 + x = 320.070304777 + 320 Combine like terms: -320 + 320 = 0 0 + x = 320.070304777 + 320 x = 320.070304777 + 320 Combine like terms: 320.070304777 + 320 = 640.070304777 x = 640.070304777 Simplifying x = 640.070304777Subproblem 2
x + -320 = -320.070304777 Simplifying x + -320 = -320.070304777 Reorder the terms: -320 + x = -320.070304777 Solving -320 + x = -320.070304777 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '320' to each side of the equation. -320 + 320 + x = -320.070304777 + 320 Combine like terms: -320 + 320 = 0 0 + x = -320.070304777 + 320 x = -320.070304777 + 320 Combine like terms: -320.070304777 + 320 = -0.070304777 x = -0.070304777 Simplifying x = -0.070304777Solution
The solution to the problem is based on the solutions from the subproblems. x = {640.070304777, -0.070304777}Solution
x = {640.070304777, -0.070304777}
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