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Simplifying 15 = 0.05x2 + -0.5x + 0.6 Reorder the terms: 15 = 0.6 + -0.5x + 0.05x2 Solving 15 = 0.6 + -0.5x + 0.05x2 Solving for variable 'x'. Combine like terms: 15 + -0.6 = 14.4 14.4 + 0.5x + -0.05x2 = 0.6 + -0.5x + 0.05x2 + -0.6 + 0.5x + -0.05x2 Reorder the terms: 14.4 + 0.5x + -0.05x2 = 0.6 + -0.6 + -0.5x + 0.5x + 0.05x2 + -0.05x2 Combine like terms: 0.6 + -0.6 = 0.0 14.4 + 0.5x + -0.05x2 = 0.0 + -0.5x + 0.5x + 0.05x2 + -0.05x2 14.4 + 0.5x + -0.05x2 = -0.5x + 0.5x + 0.05x2 + -0.05x2 Combine like terms: -0.5x + 0.5x = 0.0 14.4 + 0.5x + -0.05x2 = 0.0 + 0.05x2 + -0.05x2 14.4 + 0.5x + -0.05x2 = 0.05x2 + -0.05x2 Combine like terms: 0.05x2 + -0.05x2 = 0.00 14.4 + 0.5x + -0.05x2 = 0.00 Begin completing the square. Divide all terms by -0.05 the coefficient of the squared term: Divide each side by '-0.05'. -288 + -10x + x2 = 0 Move the constant term to the right: Add '288' to each side of the equation. -288 + -10x + 288 + x2 = 0 + 288 Reorder the terms: -288 + 288 + -10x + x2 = 0 + 288 Combine like terms: -288 + 288 = 0 0 + -10x + x2 = 0 + 288 -10x + x2 = 0 + 288 Combine like terms: 0 + 288 = 288 -10x + x2 = 288 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 288 + 25 Reorder the terms: 25 + -10x + x2 = 288 + 25 Combine like terms: 288 + 25 = 313 25 + -10x + x2 = 313 Factor a perfect square on the left side: (x + -5)(x + -5) = 313 Calculate the square root of the right side: 17.691806013 Break this problem into two subproblems by setting (x + -5) equal to 17.691806013 and -17.691806013.Subproblem 1
x + -5 = 17.691806013 Simplifying x + -5 = 17.691806013 Reorder the terms: -5 + x = 17.691806013 Solving -5 + x = 17.691806013 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 17.691806013 + 5 Combine like terms: -5 + 5 = 0 0 + x = 17.691806013 + 5 x = 17.691806013 + 5 Combine like terms: 17.691806013 + 5 = 22.691806013 x = 22.691806013 Simplifying x = 22.691806013Subproblem 2
x + -5 = -17.691806013 Simplifying x + -5 = -17.691806013 Reorder the terms: -5 + x = -17.691806013 Solving -5 + x = -17.691806013 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -17.691806013 + 5 Combine like terms: -5 + 5 = 0 0 + x = -17.691806013 + 5 x = -17.691806013 + 5 Combine like terms: -17.691806013 + 5 = -12.691806013 x = -12.691806013 Simplifying x = -12.691806013Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.691806013, -12.691806013}
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