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Simplifying 0 = 13x2 + 22x + -17 Reorder the terms: 0 = -17 + 22x + 13x2 Solving 0 = -17 + 22x + 13x2 Solving for variable 'x'. Combine like terms: 0 + 17 = 17 17 + -22x + -13x2 = -17 + 22x + 13x2 + 17 + -22x + -13x2 Reorder the terms: 17 + -22x + -13x2 = -17 + 17 + 22x + -22x + 13x2 + -13x2 Combine like terms: -17 + 17 = 0 17 + -22x + -13x2 = 0 + 22x + -22x + 13x2 + -13x2 17 + -22x + -13x2 = 22x + -22x + 13x2 + -13x2 Combine like terms: 22x + -22x = 0 17 + -22x + -13x2 = 0 + 13x2 + -13x2 17 + -22x + -13x2 = 13x2 + -13x2 Combine like terms: 13x2 + -13x2 = 0 17 + -22x + -13x2 = 0 Begin completing the square. Divide all terms by -13 the coefficient of the squared term: Divide each side by '-13'. -1.307692308 + 1.692307692x + x2 = 0 Move the constant term to the right: Add '1.307692308' to each side of the equation. -1.307692308 + 1.692307692x + 1.307692308 + x2 = 0 + 1.307692308 Reorder the terms: -1.307692308 + 1.307692308 + 1.692307692x + x2 = 0 + 1.307692308 Combine like terms: -1.307692308 + 1.307692308 = 0.000000000 0.000000000 + 1.692307692x + x2 = 0 + 1.307692308 1.692307692x + x2 = 0 + 1.307692308 Combine like terms: 0 + 1.307692308 = 1.307692308 1.692307692x + x2 = 1.307692308 The x term is 1.692307692x. Take half its coefficient (0.846153846). Square it (0.7159763311) and add it to both sides. Add '0.7159763311' to each side of the equation. 1.692307692x + 0.7159763311 + x2 = 1.307692308 + 0.7159763311 Reorder the terms: 0.7159763311 + 1.692307692x + x2 = 1.307692308 + 0.7159763311 Combine like terms: 1.307692308 + 0.7159763311 = 2.0236686391 0.7159763311 + 1.692307692x + x2 = 2.0236686391 Factor a perfect square on the left side: (x + 0.846153846)(x + 0.846153846) = 2.0236686391 Calculate the square root of the right side: 1.422557078 Break this problem into two subproblems by setting (x + 0.846153846) equal to 1.422557078 and -1.422557078.Subproblem 1
x + 0.846153846 = 1.422557078 Simplifying x + 0.846153846 = 1.422557078 Reorder the terms: 0.846153846 + x = 1.422557078 Solving 0.846153846 + x = 1.422557078 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.846153846' to each side of the equation. 0.846153846 + -0.846153846 + x = 1.422557078 + -0.846153846 Combine like terms: 0.846153846 + -0.846153846 = 0.000000000 0.000000000 + x = 1.422557078 + -0.846153846 x = 1.422557078 + -0.846153846 Combine like terms: 1.422557078 + -0.846153846 = 0.576403232 x = 0.576403232 Simplifying x = 0.576403232Subproblem 2
x + 0.846153846 = -1.422557078 Simplifying x + 0.846153846 = -1.422557078 Reorder the terms: 0.846153846 + x = -1.422557078 Solving 0.846153846 + x = -1.422557078 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.846153846' to each side of the equation. 0.846153846 + -0.846153846 + x = -1.422557078 + -0.846153846 Combine like terms: 0.846153846 + -0.846153846 = 0.000000000 0.000000000 + x = -1.422557078 + -0.846153846 x = -1.422557078 + -0.846153846 Combine like terms: -1.422557078 + -0.846153846 = -2.268710924 x = -2.268710924 Simplifying x = -2.268710924Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.576403232, -2.268710924}
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