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Simplifying -0.75(8X + -3) * 7X = -0.75 Reorder the terms: -0.75(-3 + 8X) * 7X = -0.75 Reorder the terms for easier multiplication: -0.75 * 7X(-3 + 8X) = -0.75 Multiply -0.75 * 7 -5.25X(-3 + 8X) = -0.75 (-3 * -5.25X + 8X * -5.25X) = -0.75 (15.75X + -42X2) = -0.75 Solving 15.75X + -42X2 = -0.75 Solving for variable 'X'. Reorder the terms: 0.75 + 15.75X + -42X2 = -0.75 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.75 + 15.75X + -42X2 = 0.00 Begin completing the square. Divide all terms by -42 the coefficient of the squared term: Divide each side by '-42'. -0.01785714286 + -0.375X + X2 = 0.00 Move the constant term to the right: Add '0.01785714286' to each side of the equation. -0.01785714286 + -0.375X + 0.01785714286 + X2 = 0.00 + 0.01785714286 Reorder the terms: -0.01785714286 + 0.01785714286 + -0.375X + X2 = 0.00 + 0.01785714286 Combine like terms: -0.01785714286 + 0.01785714286 = 0.00000000000 0.00000000000 + -0.375X + X2 = 0.00 + 0.01785714286 -0.375X + X2 = 0.00 + 0.01785714286 Combine like terms: 0.00 + 0.01785714286 = 0.01785714286 -0.375X + X2 = 0.01785714286 The X term is -0.375X. Take half its coefficient (-0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. -0.375X + 0.03515625 + X2 = 0.01785714286 + 0.03515625 Reorder the terms: 0.03515625 + -0.375X + X2 = 0.01785714286 + 0.03515625 Combine like terms: 0.01785714286 + 0.03515625 = 0.05301339286 0.03515625 + -0.375X + X2 = 0.05301339286 Factor a perfect square on the left side: (X + -0.1875)(X + -0.1875) = 0.05301339286 Calculate the square root of the right side: 0.230246374 Break this problem into two subproblems by setting (X + -0.1875) equal to 0.230246374 and -0.230246374.Subproblem 1
X + -0.1875 = 0.230246374 Simplifying X + -0.1875 = 0.230246374 Reorder the terms: -0.1875 + X = 0.230246374 Solving -0.1875 + X = 0.230246374 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + X = 0.230246374 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + X = 0.230246374 + 0.1875 X = 0.230246374 + 0.1875 Combine like terms: 0.230246374 + 0.1875 = 0.417746374 X = 0.417746374 Simplifying X = 0.417746374Subproblem 2
X + -0.1875 = -0.230246374 Simplifying X + -0.1875 = -0.230246374 Reorder the terms: -0.1875 + X = -0.230246374 Solving -0.1875 + X = -0.230246374 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + X = -0.230246374 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + X = -0.230246374 + 0.1875 X = -0.230246374 + 0.1875 Combine like terms: -0.230246374 + 0.1875 = -0.042746374 X = -0.042746374 Simplifying X = -0.042746374Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.417746374, -0.042746374}
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