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Simplifying 6x2 + -17x = 20x2 + -32 Reorder the terms: -17x + 6x2 = 20x2 + -32 Reorder the terms: -17x + 6x2 = -32 + 20x2 Solving -17x + 6x2 = -32 + 20x2 Solving for variable 'x'. Reorder the terms: 32 + -17x + 6x2 + -20x2 = -32 + 20x2 + 32 + -20x2 Combine like terms: 6x2 + -20x2 = -14x2 32 + -17x + -14x2 = -32 + 20x2 + 32 + -20x2 Reorder the terms: 32 + -17x + -14x2 = -32 + 32 + 20x2 + -20x2 Combine like terms: -32 + 32 = 0 32 + -17x + -14x2 = 0 + 20x2 + -20x2 32 + -17x + -14x2 = 20x2 + -20x2 Combine like terms: 20x2 + -20x2 = 0 32 + -17x + -14x2 = 0 Begin completing the square. Divide all terms by -14 the coefficient of the squared term: Divide each side by '-14'. -2.285714286 + 1.214285714x + x2 = 0 Move the constant term to the right: Add '2.285714286' to each side of the equation. -2.285714286 + 1.214285714x + 2.285714286 + x2 = 0 + 2.285714286 Reorder the terms: -2.285714286 + 2.285714286 + 1.214285714x + x2 = 0 + 2.285714286 Combine like terms: -2.285714286 + 2.285714286 = 0.000000000 0.000000000 + 1.214285714x + x2 = 0 + 2.285714286 1.214285714x + x2 = 0 + 2.285714286 Combine like terms: 0 + 2.285714286 = 2.285714286 1.214285714x + x2 = 2.285714286 The x term is 1.214285714x. Take half its coefficient (0.607142857). Square it (0.3686224488) and add it to both sides. Add '0.3686224488' to each side of the equation. 1.214285714x + 0.3686224488 + x2 = 2.285714286 + 0.3686224488 Reorder the terms: 0.3686224488 + 1.214285714x + x2 = 2.285714286 + 0.3686224488 Combine like terms: 2.285714286 + 0.3686224488 = 2.6543367348 0.3686224488 + 1.214285714x + x2 = 2.6543367348 Factor a perfect square on the left side: (x + 0.607142857)(x + 0.607142857) = 2.6543367348 Calculate the square root of the right side: 1.629213533 Break this problem into two subproblems by setting (x + 0.607142857) equal to 1.629213533 and -1.629213533.Subproblem 1
x + 0.607142857 = 1.629213533 Simplifying x + 0.607142857 = 1.629213533 Reorder the terms: 0.607142857 + x = 1.629213533 Solving 0.607142857 + x = 1.629213533 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.607142857' to each side of the equation. 0.607142857 + -0.607142857 + x = 1.629213533 + -0.607142857 Combine like terms: 0.607142857 + -0.607142857 = 0.000000000 0.000000000 + x = 1.629213533 + -0.607142857 x = 1.629213533 + -0.607142857 Combine like terms: 1.629213533 + -0.607142857 = 1.022070676 x = 1.022070676 Simplifying x = 1.022070676Subproblem 2
x + 0.607142857 = -1.629213533 Simplifying x + 0.607142857 = -1.629213533 Reorder the terms: 0.607142857 + x = -1.629213533 Solving 0.607142857 + x = -1.629213533 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.607142857' to each side of the equation. 0.607142857 + -0.607142857 + x = -1.629213533 + -0.607142857 Combine like terms: 0.607142857 + -0.607142857 = 0.000000000 0.000000000 + x = -1.629213533 + -0.607142857 x = -1.629213533 + -0.607142857 Combine like terms: -1.629213533 + -0.607142857 = -2.23635639 x = -2.23635639 Simplifying x = -2.23635639Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.022070676, -2.23635639}
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