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Simplifying 5x2 + -50x + 75 = 0 Reorder the terms: 75 + -50x + 5x2 = 0 Solving 75 + -50x + 5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(15 + -10x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(15 + -10x + x2)' equal to zero and attempt to solve: Simplifying 15 + -10x + x2 = 0 Solving 15 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + -10x + -15 + x2 = 0 + -15 Reorder the terms: 15 + -15 + -10x + x2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -10x + x2 = 0 + -15 -10x + x2 = 0 + -15 Combine like terms: 0 + -15 = -15 -10x + x2 = -15 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -15 + 25 Reorder the terms: 25 + -10x + x2 = -15 + 25 Combine like terms: -15 + 25 = 10 25 + -10x + x2 = 10 Factor a perfect square on the left side: (x + -5)(x + -5) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (x + -5) equal to 3.16227766 and -3.16227766.Subproblem 1
x + -5 = 3.16227766 Simplifying x + -5 = 3.16227766 Reorder the terms: -5 + x = 3.16227766 Solving -5 + x = 3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 3.16227766 + 5 Combine like terms: -5 + 5 = 0 0 + x = 3.16227766 + 5 x = 3.16227766 + 5 Combine like terms: 3.16227766 + 5 = 8.16227766 x = 8.16227766 Simplifying x = 8.16227766Subproblem 2
x + -5 = -3.16227766 Simplifying x + -5 = -3.16227766 Reorder the terms: -5 + x = -3.16227766 Solving -5 + x = -3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -3.16227766 + 5 Combine like terms: -5 + 5 = 0 0 + x = -3.16227766 + 5 x = -3.16227766 + 5 Combine like terms: -3.16227766 + 5 = 1.83772234 x = 1.83772234 Simplifying x = 1.83772234Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.16227766, 1.83772234}Solution
x = {8.16227766, 1.83772234}
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