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Simplifying x2 + 300x + -12.6 = 0 Reorder the terms: -12.6 + 300x + x2 = 0 Solving -12.6 + 300x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '12.6' to each side of the equation. -12.6 + 300x + 12.6 + x2 = 0 + 12.6 Reorder the terms: -12.6 + 12.6 + 300x + x2 = 0 + 12.6 Combine like terms: -12.6 + 12.6 = 0.0 0.0 + 300x + x2 = 0 + 12.6 300x + x2 = 0 + 12.6 Combine like terms: 0 + 12.6 = 12.6 300x + x2 = 12.6 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 = 12.6 + 22500 Reorder the terms: 22500 + 300x + x2 = 12.6 + 22500 Combine like terms: 12.6 + 22500 = 22512.6 22500 + 300x + x2 = 22512.6 Factor a perfect square on the left side: (x + 150)(x + 150) = 22512.6 Calculate the square root of the right side: 150.041994122 Break this problem into two subproblems by setting (x + 150) equal to 150.041994122 and -150.041994122.Subproblem 1
x + 150 = 150.041994122 Simplifying x + 150 = 150.041994122 Reorder the terms: 150 + x = 150.041994122 Solving 150 + x = 150.041994122 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 = 150.041994122 + -150 Combine like terms: 150 + -150 = 0 0 + x = 150.041994122 + -150 x = 150.041994122 + -150 Combine like terms: 150.041994122 + -150 = 0.041994122 x = 0.041994122 Simplifying x = 0.041994122Subproblem 2
x + 150 = -150.041994122 Simplifying x + 150 = -150.041994122 Reorder the terms: 150 + x = -150.041994122 Solving 150 + x = -150.041994122 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 = -150.041994122 + -150 Combine like terms: 150 + -150 = 0 0 + x = -150.041994122 + -150 x = -150.041994122 + -150 Combine like terms: -150.041994122 + -150 = -300.041994122 x = -300.041994122 Simplifying x = -300.041994122Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.041994122, -300.041994122}
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