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Simplifying x2 + -200x + 9200 = 0 Reorder the terms: 9200 + -200x + x2 = 0 Solving 9200 + -200x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-9200' to each side of the equation. 9200 + -200x + -9200 + x2 = 0 + -9200 Reorder the terms: 9200 + -9200 + -200x + x2 = 0 + -9200 Combine like terms: 9200 + -9200 = 0 0 + -200x + x2 = 0 + -9200 -200x + x2 = 0 + -9200 Combine like terms: 0 + -9200 = -9200 -200x + x2 = -9200 The x term is -200x. Take half its coefficient (-100). Square it (10000) and add it to both sides. Add '10000' to each side of the equation. -200x + 10000 + x2 = -9200 + 10000 Reorder the terms: 10000 + -200x + x2 = -9200 + 10000 Combine like terms: -9200 + 10000 = 800 10000 + -200x + x2 = 800 Factor a perfect square on the left side: (x + -100)(x + -100) = 800 Calculate the square root of the right side: 28.284271247 Break this problem into two subproblems by setting (x + -100) equal to 28.284271247 and -28.284271247.Subproblem 1
x + -100 = 28.284271247 Simplifying x + -100 = 28.284271247 Reorder the terms: -100 + x = 28.284271247 Solving -100 + x = 28.284271247 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = 28.284271247 + 100 Combine like terms: -100 + 100 = 0 0 + x = 28.284271247 + 100 x = 28.284271247 + 100 Combine like terms: 28.284271247 + 100 = 128.284271247 x = 128.284271247 Simplifying x = 128.284271247Subproblem 2
x + -100 = -28.284271247 Simplifying x + -100 = -28.284271247 Reorder the terms: -100 + x = -28.284271247 Solving -100 + x = -28.284271247 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = -28.284271247 + 100 Combine like terms: -100 + 100 = 0 0 + x = -28.284271247 + 100 x = -28.284271247 + 100 Combine like terms: -28.284271247 + 100 = 71.715728753 x = 71.715728753 Simplifying x = 71.715728753Solution
The solution to the problem is based on the solutions from the subproblems. x = {128.284271247, 71.715728753}
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