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Simplifying x + -4(x + -7) * 8x = 6 Reorder the terms: x + -4(-7 + x) * 8x = 6 Reorder the terms for easier multiplication: x + -4 * 8x(-7 + x) = 6 Multiply -4 * 8 x + -32x(-7 + x) = 6 x + (-7 * -32x + x * -32x) = 6 x + (224x + -32x2) = 6 Combine like terms: x + 224x = 225x 225x + -32x2 = 6 Solving 225x + -32x2 = 6 Solving for variable 'x'. Reorder the terms: -6 + 225x + -32x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + 225x + -32x2 = 0 Begin completing the square. Divide all terms by -32 the coefficient of the squared term: Divide each side by '-32'. 0.1875 + -7.03125x + x2 = 0 Move the constant term to the right: Add '-0.1875' to each side of the equation. 0.1875 + -7.03125x + -0.1875 + x2 = 0 + -0.1875 Reorder the terms: 0.1875 + -0.1875 + -7.03125x + x2 = 0 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + -7.03125x + x2 = 0 + -0.1875 -7.03125x + x2 = 0 + -0.1875 Combine like terms: 0 + -0.1875 = -0.1875 -7.03125x + x2 = -0.1875 The x term is -7.03125x. Take half its coefficient (-3.515625). Square it (12.35961914) and add it to both sides. Add '12.35961914' to each side of the equation. -7.03125x + 12.35961914 + x2 = -0.1875 + 12.35961914 Reorder the terms: 12.35961914 + -7.03125x + x2 = -0.1875 + 12.35961914 Combine like terms: -0.1875 + 12.35961914 = 12.17211914 12.35961914 + -7.03125x + x2 = 12.17211914 Factor a perfect square on the left side: (x + -3.515625)(x + -3.515625) = 12.17211914 Calculate the square root of the right side: 3.488856423 Break this problem into two subproblems by setting (x + -3.515625) equal to 3.488856423 and -3.488856423.Subproblem 1
x + -3.515625 = 3.488856423 Simplifying x + -3.515625 = 3.488856423 Reorder the terms: -3.515625 + x = 3.488856423 Solving -3.515625 + x = 3.488856423 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.515625' to each side of the equation. -3.515625 + 3.515625 + x = 3.488856423 + 3.515625 Combine like terms: -3.515625 + 3.515625 = 0.000000 0.000000 + x = 3.488856423 + 3.515625 x = 3.488856423 + 3.515625 Combine like terms: 3.488856423 + 3.515625 = 7.004481423 x = 7.004481423 Simplifying x = 7.004481423Subproblem 2
x + -3.515625 = -3.488856423 Simplifying x + -3.515625 = -3.488856423 Reorder the terms: -3.515625 + x = -3.488856423 Solving -3.515625 + x = -3.488856423 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.515625' to each side of the equation. -3.515625 + 3.515625 + x = -3.488856423 + 3.515625 Combine like terms: -3.515625 + 3.515625 = 0.000000 0.000000 + x = -3.488856423 + 3.515625 x = -3.488856423 + 3.515625 Combine like terms: -3.488856423 + 3.515625 = 0.026768577 x = 0.026768577 Simplifying x = 0.026768577Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.004481423, 0.026768577}
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