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Simplifying -8x(x + -7) + -6 = 5 Reorder the terms: -8x(-7 + x) + -6 = 5 (-7 * -8x + x * -8x) + -6 = 5 (56x + -8x2) + -6 = 5 Reorder the terms: -6 + 56x + -8x2 = 5 Solving -6 + 56x + -8x2 = 5 Solving for variable 'x'. Reorder the terms: -6 + -5 + 56x + -8x2 = 5 + -5 Combine like terms: -6 + -5 = -11 -11 + 56x + -8x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -11 + 56x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 1.375 + -7x + x2 = 0 Move the constant term to the right: Add '-1.375' to each side of the equation. 1.375 + -7x + -1.375 + x2 = 0 + -1.375 Reorder the terms: 1.375 + -1.375 + -7x + x2 = 0 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + -7x + x2 = 0 + -1.375 -7x + x2 = 0 + -1.375 Combine like terms: 0 + -1.375 = -1.375 -7x + x2 = -1.375 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = -1.375 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -1.375 + 12.25 Combine like terms: -1.375 + 12.25 = 10.875 12.25 + -7x + x2 = 10.875 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 10.875 Calculate the square root of the right side: 3.29772649 Break this problem into two subproblems by setting (x + -3.5) equal to 3.29772649 and -3.29772649.Subproblem 1
x + -3.5 = 3.29772649 Simplifying x + -3.5 = 3.29772649 Reorder the terms: -3.5 + x = 3.29772649 Solving -3.5 + x = 3.29772649 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 3.29772649 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 3.29772649 + 3.5 x = 3.29772649 + 3.5 Combine like terms: 3.29772649 + 3.5 = 6.79772649 x = 6.79772649 Simplifying x = 6.79772649Subproblem 2
x + -3.5 = -3.29772649 Simplifying x + -3.5 = -3.29772649 Reorder the terms: -3.5 + x = -3.29772649 Solving -3.5 + x = -3.29772649 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -3.29772649 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -3.29772649 + 3.5 x = -3.29772649 + 3.5 Combine like terms: -3.29772649 + 3.5 = 0.20227351 x = 0.20227351 Simplifying x = 0.20227351Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.79772649, 0.20227351}
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