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Simplifying 35x2 + -2x + -6 = 0 Reorder the terms: -6 + -2x + 35x2 = 0 Solving -6 + -2x + 35x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. -0.1714285714 + -0.05714285714x + x2 = 0 Move the constant term to the right: Add '0.1714285714' to each side of the equation. -0.1714285714 + -0.05714285714x + 0.1714285714 + x2 = 0 + 0.1714285714 Reorder the terms: -0.1714285714 + 0.1714285714 + -0.05714285714x + x2 = 0 + 0.1714285714 Combine like terms: -0.1714285714 + 0.1714285714 = 0.0000000000 0.0000000000 + -0.05714285714x + x2 = 0 + 0.1714285714 -0.05714285714x + x2 = 0 + 0.1714285714 Combine like terms: 0 + 0.1714285714 = 0.1714285714 -0.05714285714x + x2 = 0.1714285714 The x term is -0.05714285714x. Take half its coefficient (-0.02857142857). Square it (0.0008163265305) and add it to both sides. Add '0.0008163265305' to each side of the equation. -0.05714285714x + 0.0008163265305 + x2 = 0.1714285714 + 0.0008163265305 Reorder the terms: 0.0008163265305 + -0.05714285714x + x2 = 0.1714285714 + 0.0008163265305 Combine like terms: 0.1714285714 + 0.0008163265305 = 0.1722448979305 0.0008163265305 + -0.05714285714x + x2 = 0.1722448979305 Factor a perfect square on the left side: (x + -0.02857142857)(x + -0.02857142857) = 0.1722448979305 Calculate the square root of the right side: 0.415023973 Break this problem into two subproblems by setting (x + -0.02857142857) equal to 0.415023973 and -0.415023973.Subproblem 1
x + -0.02857142857 = 0.415023973 Simplifying x + -0.02857142857 = 0.415023973 Reorder the terms: -0.02857142857 + x = 0.415023973 Solving -0.02857142857 + x = 0.415023973 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.02857142857' to each side of the equation. -0.02857142857 + 0.02857142857 + x = 0.415023973 + 0.02857142857 Combine like terms: -0.02857142857 + 0.02857142857 = 0.00000000000 0.00000000000 + x = 0.415023973 + 0.02857142857 x = 0.415023973 + 0.02857142857 Combine like terms: 0.415023973 + 0.02857142857 = 0.44359540157 x = 0.44359540157 Simplifying x = 0.44359540157Subproblem 2
x + -0.02857142857 = -0.415023973 Simplifying x + -0.02857142857 = -0.415023973 Reorder the terms: -0.02857142857 + x = -0.415023973 Solving -0.02857142857 + x = -0.415023973 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.02857142857' to each side of the equation. -0.02857142857 + 0.02857142857 + x = -0.415023973 + 0.02857142857 Combine like terms: -0.02857142857 + 0.02857142857 = 0.00000000000 0.00000000000 + x = -0.415023973 + 0.02857142857 x = -0.415023973 + 0.02857142857 Combine like terms: -0.415023973 + 0.02857142857 = -0.38645254443 x = -0.38645254443 Simplifying x = -0.38645254443Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.44359540157, -0.38645254443}
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