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Simplifying 10x2 + -67x + -69 = 0 Reorder the terms: -69 + -67x + 10x2 = 0 Solving -69 + -67x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -6.9 + -6.7x + x2 = 0 Move the constant term to the right: Add '6.9' to each side of the equation. -6.9 + -6.7x + 6.9 + x2 = 0 + 6.9 Reorder the terms: -6.9 + 6.9 + -6.7x + x2 = 0 + 6.9 Combine like terms: -6.9 + 6.9 = 0.0 0.0 + -6.7x + x2 = 0 + 6.9 -6.7x + x2 = 0 + 6.9 Combine like terms: 0 + 6.9 = 6.9 -6.7x + x2 = 6.9 The x term is -6.7x. Take half its coefficient (-3.35). Square it (11.2225) and add it to both sides. Add '11.2225' to each side of the equation. -6.7x + 11.2225 + x2 = 6.9 + 11.2225 Reorder the terms: 11.2225 + -6.7x + x2 = 6.9 + 11.2225 Combine like terms: 6.9 + 11.2225 = 18.1225 11.2225 + -6.7x + x2 = 18.1225 Factor a perfect square on the left side: (x + -3.35)(x + -3.35) = 18.1225 Calculate the square root of the right side: 4.257052971 Break this problem into two subproblems by setting (x + -3.35) equal to 4.257052971 and -4.257052971.Subproblem 1
x + -3.35 = 4.257052971 Simplifying x + -3.35 = 4.257052971 Reorder the terms: -3.35 + x = 4.257052971 Solving -3.35 + x = 4.257052971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.35' to each side of the equation. -3.35 + 3.35 + x = 4.257052971 + 3.35 Combine like terms: -3.35 + 3.35 = 0.00 0.00 + x = 4.257052971 + 3.35 x = 4.257052971 + 3.35 Combine like terms: 4.257052971 + 3.35 = 7.607052971 x = 7.607052971 Simplifying x = 7.607052971Subproblem 2
x + -3.35 = -4.257052971 Simplifying x + -3.35 = -4.257052971 Reorder the terms: -3.35 + x = -4.257052971 Solving -3.35 + x = -4.257052971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.35' to each side of the equation. -3.35 + 3.35 + x = -4.257052971 + 3.35 Combine like terms: -3.35 + 3.35 = 0.00 0.00 + x = -4.257052971 + 3.35 x = -4.257052971 + 3.35 Combine like terms: -4.257052971 + 3.35 = -0.907052971 x = -0.907052971 Simplifying x = -0.907052971Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.607052971, -0.907052971}
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