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Simplifying 15x2 + -150x = x + -5 Reorder the terms: -150x + 15x2 = x + -5 Reorder the terms: -150x + 15x2 = -5 + x Solving -150x + 15x2 = -5 + x Solving for variable 'x'. Reorder the terms: 5 + -150x + -1x + 15x2 = -5 + x + 5 + -1x Combine like terms: -150x + -1x = -151x 5 + -151x + 15x2 = -5 + x + 5 + -1x Reorder the terms: 5 + -151x + 15x2 = -5 + 5 + x + -1x Combine like terms: -5 + 5 = 0 5 + -151x + 15x2 = 0 + x + -1x 5 + -151x + 15x2 = x + -1x Combine like terms: x + -1x = 0 5 + -151x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. 0.3333333333 + -10.06666667x + x2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + -10.06666667x + -0.3333333333 + x2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + -10.06666667x + x2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + -10.06666667x + x2 = 0 + -0.3333333333 -10.06666667x + x2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 -10.06666667x + x2 = -0.3333333333 The x term is -10.06666667x. Take half its coefficient (-5.033333335). Square it (25.33444446) and add it to both sides. Add '25.33444446' to each side of the equation. -10.06666667x + 25.33444446 + x2 = -0.3333333333 + 25.33444446 Reorder the terms: 25.33444446 + -10.06666667x + x2 = -0.3333333333 + 25.33444446 Combine like terms: -0.3333333333 + 25.33444446 = 25.0011111267 25.33444446 + -10.06666667x + x2 = 25.0011111267 Factor a perfect square on the left side: (x + -5.033333335)(x + -5.033333335) = 25.0011111267 Calculate the square root of the right side: 5.000111111 Break this problem into two subproblems by setting (x + -5.033333335) equal to 5.000111111 and -5.000111111.Subproblem 1
x + -5.033333335 = 5.000111111 Simplifying x + -5.033333335 = 5.000111111 Reorder the terms: -5.033333335 + x = 5.000111111 Solving -5.033333335 + x = 5.000111111 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.033333335' to each side of the equation. -5.033333335 + 5.033333335 + x = 5.000111111 + 5.033333335 Combine like terms: -5.033333335 + 5.033333335 = 0.000000000 0.000000000 + x = 5.000111111 + 5.033333335 x = 5.000111111 + 5.033333335 Combine like terms: 5.000111111 + 5.033333335 = 10.033444446 x = 10.033444446 Simplifying x = 10.033444446Subproblem 2
x + -5.033333335 = -5.000111111 Simplifying x + -5.033333335 = -5.000111111 Reorder the terms: -5.033333335 + x = -5.000111111 Solving -5.033333335 + x = -5.000111111 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.033333335' to each side of the equation. -5.033333335 + 5.033333335 + x = -5.000111111 + 5.033333335 Combine like terms: -5.033333335 + 5.033333335 = 0.000000000 0.000000000 + x = -5.000111111 + 5.033333335 x = -5.000111111 + 5.033333335 Combine like terms: -5.000111111 + 5.033333335 = 0.033222224 x = 0.033222224 Simplifying x = 0.033222224Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.033444446, 0.033222224}
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