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Simplifying 15x + -10 = 4 + -100x(4x + -7) Reorder the terms: -10 + 15x = 4 + -100x(4x + -7) Reorder the terms: -10 + 15x = 4 + -100x(-7 + 4x) -10 + 15x = 4 + (-7 * -100x + 4x * -100x) -10 + 15x = 4 + (700x + -400x2) Solving -10 + 15x = 4 + 700x + -400x2 Solving for variable 'x'. Reorder the terms: -10 + -4 + 15x + -700x + 400x2 = 4 + 700x + -400x2 + -4 + -700x + 400x2 Combine like terms: -10 + -4 = -14 -14 + 15x + -700x + 400x2 = 4 + 700x + -400x2 + -4 + -700x + 400x2 Combine like terms: 15x + -700x = -685x -14 + -685x + 400x2 = 4 + 700x + -400x2 + -4 + -700x + 400x2 Reorder the terms: -14 + -685x + 400x2 = 4 + -4 + 700x + -700x + -400x2 + 400x2 Combine like terms: 4 + -4 = 0 -14 + -685x + 400x2 = 0 + 700x + -700x + -400x2 + 400x2 -14 + -685x + 400x2 = 700x + -700x + -400x2 + 400x2 Combine like terms: 700x + -700x = 0 -14 + -685x + 400x2 = 0 + -400x2 + 400x2 -14 + -685x + 400x2 = -400x2 + 400x2 Combine like terms: -400x2 + 400x2 = 0 -14 + -685x + 400x2 = 0 Begin completing the square. Divide all terms by 400 the coefficient of the squared term: Divide each side by '400'. -0.035 + -1.7125x + x2 = 0 Move the constant term to the right: Add '0.035' to each side of the equation. -0.035 + -1.7125x + 0.035 + x2 = 0 + 0.035 Reorder the terms: -0.035 + 0.035 + -1.7125x + x2 = 0 + 0.035 Combine like terms: -0.035 + 0.035 = 0.000 0.000 + -1.7125x + x2 = 0 + 0.035 -1.7125x + x2 = 0 + 0.035 Combine like terms: 0 + 0.035 = 0.035 -1.7125x + x2 = 0.035 The x term is -1.7125x. Take half its coefficient (-0.85625). Square it (0.7331640625) and add it to both sides. Add '0.7331640625' to each side of the equation. -1.7125x + 0.7331640625 + x2 = 0.035 + 0.7331640625 Reorder the terms: 0.7331640625 + -1.7125x + x2 = 0.035 + 0.7331640625 Combine like terms: 0.035 + 0.7331640625 = 0.7681640625 0.7331640625 + -1.7125x + x2 = 0.7681640625 Factor a perfect square on the left side: (x + -0.85625)(x + -0.85625) = 0.7681640625 Calculate the square root of the right side: 0.876449692 Break this problem into two subproblems by setting (x + -0.85625) equal to 0.876449692 and -0.876449692.Subproblem 1
x + -0.85625 = 0.876449692 Simplifying x + -0.85625 = 0.876449692 Reorder the terms: -0.85625 + x = 0.876449692 Solving -0.85625 + x = 0.876449692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.85625' to each side of the equation. -0.85625 + 0.85625 + x = 0.876449692 + 0.85625 Combine like terms: -0.85625 + 0.85625 = 0.00000 0.00000 + x = 0.876449692 + 0.85625 x = 0.876449692 + 0.85625 Combine like terms: 0.876449692 + 0.85625 = 1.732699692 x = 1.732699692 Simplifying x = 1.732699692Subproblem 2
x + -0.85625 = -0.876449692 Simplifying x + -0.85625 = -0.876449692 Reorder the terms: -0.85625 + x = -0.876449692 Solving -0.85625 + x = -0.876449692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.85625' to each side of the equation. -0.85625 + 0.85625 + x = -0.876449692 + 0.85625 Combine like terms: -0.85625 + 0.85625 = 0.00000 0.00000 + x = -0.876449692 + 0.85625 x = -0.876449692 + 0.85625 Combine like terms: -0.876449692 + 0.85625 = -0.020199692 x = -0.020199692 Simplifying x = -0.020199692Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.732699692, -0.020199692}
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