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Simplifying 8x2 + -55x + -42 = 0 Reorder the terms: -42 + -55x + 8x2 = 0 Solving -42 + -55x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -5.25 + -6.875x + x2 = 0 Move the constant term to the right: Add '5.25' to each side of the equation. -5.25 + -6.875x + 5.25 + x2 = 0 + 5.25 Reorder the terms: -5.25 + 5.25 + -6.875x + x2 = 0 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + -6.875x + x2 = 0 + 5.25 -6.875x + x2 = 0 + 5.25 Combine like terms: 0 + 5.25 = 5.25 -6.875x + x2 = 5.25 The x term is -6.875x. Take half its coefficient (-3.4375). Square it (11.81640625) and add it to both sides. Add '11.81640625' to each side of the equation. -6.875x + 11.81640625 + x2 = 5.25 + 11.81640625 Reorder the terms: 11.81640625 + -6.875x + x2 = 5.25 + 11.81640625 Combine like terms: 5.25 + 11.81640625 = 17.06640625 11.81640625 + -6.875x + x2 = 17.06640625 Factor a perfect square on the left side: (x + -3.4375)(x + -3.4375) = 17.06640625 Calculate the square root of the right side: 4.131150717 Break this problem into two subproblems by setting (x + -3.4375) equal to 4.131150717 and -4.131150717.Subproblem 1
x + -3.4375 = 4.131150717 Simplifying x + -3.4375 = 4.131150717 Reorder the terms: -3.4375 + x = 4.131150717 Solving -3.4375 + x = 4.131150717 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.4375' to each side of the equation. -3.4375 + 3.4375 + x = 4.131150717 + 3.4375 Combine like terms: -3.4375 + 3.4375 = 0.0000 0.0000 + x = 4.131150717 + 3.4375 x = 4.131150717 + 3.4375 Combine like terms: 4.131150717 + 3.4375 = 7.568650717 x = 7.568650717 Simplifying x = 7.568650717Subproblem 2
x + -3.4375 = -4.131150717 Simplifying x + -3.4375 = -4.131150717 Reorder the terms: -3.4375 + x = -4.131150717 Solving -3.4375 + x = -4.131150717 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.4375' to each side of the equation. -3.4375 + 3.4375 + x = -4.131150717 + 3.4375 Combine like terms: -3.4375 + 3.4375 = 0.0000 0.0000 + x = -4.131150717 + 3.4375 x = -4.131150717 + 3.4375 Combine like terms: -4.131150717 + 3.4375 = -0.693650717 x = -0.693650717 Simplifying x = -0.693650717Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.568650717, -0.693650717}
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