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Simplifying 300x + -100 = x2 Reorder the terms: -100 + 300x = x2 Solving -100 + 300x = x2 Solving for variable 'x'. Combine like terms: x2 + -1x2 = 0 -100 + 300x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 100 + -300x + x2 = 0 Move the constant term to the right: Add '-100' to each side of the equation. 100 + -300x + -100 + x2 = 0 + -100 Reorder the terms: 100 + -100 + -300x + x2 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + -300x + x2 = 0 + -100 -300x + x2 = 0 + -100 Combine like terms: 0 + -100 = -100 -300x + x2 = -100 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 = -100 + 22500 Reorder the terms: 22500 + -300x + x2 = -100 + 22500 Combine like terms: -100 + 22500 = 22400 22500 + -300x + x2 = 22400 Factor a perfect square on the left side: (x + -150)(x + -150) = 22400 Calculate the square root of the right side: 149.666295471 Break this problem into two subproblems by setting (x + -150) equal to 149.666295471 and -149.666295471.Subproblem 1
x + -150 = 149.666295471 Simplifying x + -150 = 149.666295471 Reorder the terms: -150 + x = 149.666295471 Solving -150 + x = 149.666295471 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 = 149.666295471 + 150 Combine like terms: -150 + 150 = 0 0 + x = 149.666295471 + 150 x = 149.666295471 + 150 Combine like terms: 149.666295471 + 150 = 299.666295471 x = 299.666295471 Simplifying x = 299.666295471Subproblem 2
x + -150 = -149.666295471 Simplifying x + -150 = -149.666295471 Reorder the terms: -150 + x = -149.666295471 Solving -150 + x = -149.666295471 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 = -149.666295471 + 150 Combine like terms: -150 + 150 = 0 0 + x = -149.666295471 + 150 x = -149.666295471 + 150 Combine like terms: -149.666295471 + 150 = 0.333704529 x = 0.333704529 Simplifying x = 0.333704529Solution
The solution to the problem is based on the solutions from the subproblems. x = {299.666295471, 0.333704529}
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