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Simplifying 5x2 + -100x = 28 Reorder the terms: -100x + 5x2 = 28 Solving -100x + 5x2 = 28 Solving for variable 'x'. Reorder the terms: -28 + -100x + 5x2 = 28 + -28 Combine like terms: 28 + -28 = 0 -28 + -100x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -5.6 + -20x + x2 = 0 Move the constant term to the right: Add '5.6' to each side of the equation. -5.6 + -20x + 5.6 + x2 = 0 + 5.6 Reorder the terms: -5.6 + 5.6 + -20x + x2 = 0 + 5.6 Combine like terms: -5.6 + 5.6 = 0.0 0.0 + -20x + x2 = 0 + 5.6 -20x + x2 = 0 + 5.6 Combine like terms: 0 + 5.6 = 5.6 -20x + x2 = 5.6 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 = 5.6 + 100 Reorder the terms: 100 + -20x + x2 = 5.6 + 100 Combine like terms: 5.6 + 100 = 105.6 100 + -20x + x2 = 105.6 Factor a perfect square on the left side: (x + -10)(x + -10) = 105.6 Calculate the square root of the right side: 10.276186063 Break this problem into two subproblems by setting (x + -10) equal to 10.276186063 and -10.276186063.Subproblem 1
x + -10 = 10.276186063 Simplifying x + -10 = 10.276186063 Reorder the terms: -10 + x = 10.276186063 Solving -10 + x = 10.276186063 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 = 10.276186063 + 10 Combine like terms: -10 + 10 = 0 0 + x = 10.276186063 + 10 x = 10.276186063 + 10 Combine like terms: 10.276186063 + 10 = 20.276186063 x = 20.276186063 Simplifying x = 20.276186063Subproblem 2
x + -10 = -10.276186063 Simplifying x + -10 = -10.276186063 Reorder the terms: -10 + x = -10.276186063 Solving -10 + x = -10.276186063 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 = -10.276186063 + 10 Combine like terms: -10 + 10 = 0 0 + x = -10.276186063 + 10 x = -10.276186063 + 10 Combine like terms: -10.276186063 + 10 = -0.276186063 x = -0.276186063 Simplifying x = -0.276186063Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.276186063, -0.276186063}
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