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Simplifying x2 + -300x + 19005 = 0 Reorder the terms: 19005 + -300x + x2 = 0 Solving 19005 + -300x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-19005' to each side of the equation. 19005 + -300x + -19005 + x2 = 0 + -19005 Reorder the terms: 19005 + -19005 + -300x + x2 = 0 + -19005 Combine like terms: 19005 + -19005 = 0 0 + -300x + x2 = 0 + -19005 -300x + x2 = 0 + -19005 Combine like terms: 0 + -19005 = -19005 -300x + x2 = -19005 The x term is -300x. Take half its coefficient (-150). Square it (22500) and add it to both sides. Add '22500' to each side of the equation. -300x + 22500 + x2 = -19005 + 22500 Reorder the terms: 22500 + -300x + x2 = -19005 + 22500 Combine like terms: -19005 + 22500 = 3495 22500 + -300x + x2 = 3495 Factor a perfect square on the left side: (x + -150)(x + -150) = 3495 Calculate the square root of the right side: 59.118525015 Break this problem into two subproblems by setting (x + -150) equal to 59.118525015 and -59.118525015.Subproblem 1
x + -150 = 59.118525015 Simplifying x + -150 = 59.118525015 Reorder the terms: -150 + x = 59.118525015 Solving -150 + x = 59.118525015 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '150' to each side of the equation. -150 + 150 + x = 59.118525015 + 150 Combine like terms: -150 + 150 = 0 0 + x = 59.118525015 + 150 x = 59.118525015 + 150 Combine like terms: 59.118525015 + 150 = 209.118525015 x = 209.118525015 Simplifying x = 209.118525015Subproblem 2
x + -150 = -59.118525015 Simplifying x + -150 = -59.118525015 Reorder the terms: -150 + x = -59.118525015 Solving -150 + x = -59.118525015 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '150' to each side of the equation. -150 + 150 + x = -59.118525015 + 150 Combine like terms: -150 + 150 = 0 0 + x = -59.118525015 + 150 x = -59.118525015 + 150 Combine like terms: -59.118525015 + 150 = 90.881474985 x = 90.881474985 Simplifying x = 90.881474985Solution
The solution to the problem is based on the solutions from the subproblems. x = {209.118525015, 90.881474985}
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