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Simplifying x2 + -20x + 65 = 0 Reorder the terms: 65 + -20x + x2 = 0 Solving 65 + -20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-65' to each side of the equation. 65 + -20x + -65 + x2 = 0 + -65 Reorder the terms: 65 + -65 + -20x + x2 = 0 + -65 Combine like terms: 65 + -65 = 0 0 + -20x + x2 = 0 + -65 -20x + x2 = 0 + -65 Combine like terms: 0 + -65 = -65 -20x + x2 = -65 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = -65 + 100 Reorder the terms: 100 + -20x + x2 = -65 + 100 Combine like terms: -65 + 100 = 35 100 + -20x + x2 = 35 Factor a perfect square on the left side: (x + -10)(x + -10) = 35 Calculate the square root of the right side: 5.916079783 Break this problem into two subproblems by setting (x + -10) equal to 5.916079783 and -5.916079783.Subproblem 1
x + -10 = 5.916079783 Simplifying x + -10 = 5.916079783 Reorder the terms: -10 + x = 5.916079783 Solving -10 + x = 5.916079783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 5.916079783 + 10 Combine like terms: -10 + 10 = 0 0 + x = 5.916079783 + 10 x = 5.916079783 + 10 Combine like terms: 5.916079783 + 10 = 15.916079783 x = 15.916079783 Simplifying x = 15.916079783Subproblem 2
x + -10 = -5.916079783 Simplifying x + -10 = -5.916079783 Reorder the terms: -10 + x = -5.916079783 Solving -10 + x = -5.916079783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -5.916079783 + 10 Combine like terms: -10 + 10 = 0 0 + x = -5.916079783 + 10 x = -5.916079783 + 10 Combine like terms: -5.916079783 + 10 = 4.083920217 x = 4.083920217 Simplifying x = 4.083920217Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.916079783, 4.083920217}
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