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Simplifying 35x2 + 19x * 8 = 6 Reorder the terms for easier multiplication: 35x2 + 19 * 8x = 6 Multiply 19 * 8 35x2 + 152x = 6 Reorder the terms: 152x + 35x2 = 6 Solving 152x + 35x2 = 6 Solving for variable 'x'. Reorder the terms: -6 + 152x + 35x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + 152x + 35x2 = 0 Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. -0.1714285714 + 4.342857143x + x2 = 0 Move the constant term to the right: Add '0.1714285714' to each side of the equation. -0.1714285714 + 4.342857143x + 0.1714285714 + x2 = 0 + 0.1714285714 Reorder the terms: -0.1714285714 + 0.1714285714 + 4.342857143x + x2 = 0 + 0.1714285714 Combine like terms: -0.1714285714 + 0.1714285714 = 0.0000000000 0.0000000000 + 4.342857143x + x2 = 0 + 0.1714285714 4.342857143x + x2 = 0 + 0.1714285714 Combine like terms: 0 + 0.1714285714 = 0.1714285714 4.342857143x + x2 = 0.1714285714 The x term is 4.342857143x. Take half its coefficient (2.171428572). Square it (4.715102043) and add it to both sides. Add '4.715102043' to each side of the equation. 4.342857143x + 4.715102043 + x2 = 0.1714285714 + 4.715102043 Reorder the terms: 4.715102043 + 4.342857143x + x2 = 0.1714285714 + 4.715102043 Combine like terms: 0.1714285714 + 4.715102043 = 4.8865306144 4.715102043 + 4.342857143x + x2 = 4.8865306144 Factor a perfect square on the left side: (x + 2.171428572)(x + 2.171428572) = 4.8865306144 Calculate the square root of the right side: 2.210549844 Break this problem into two subproblems by setting (x + 2.171428572) equal to 2.210549844 and -2.210549844.Subproblem 1
x + 2.171428572 = 2.210549844 Simplifying x + 2.171428572 = 2.210549844 Reorder the terms: 2.171428572 + x = 2.210549844 Solving 2.171428572 + x = 2.210549844 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.171428572' to each side of the equation. 2.171428572 + -2.171428572 + x = 2.210549844 + -2.171428572 Combine like terms: 2.171428572 + -2.171428572 = 0.000000000 0.000000000 + x = 2.210549844 + -2.171428572 x = 2.210549844 + -2.171428572 Combine like terms: 2.210549844 + -2.171428572 = 0.039121272 x = 0.039121272 Simplifying x = 0.039121272Subproblem 2
x + 2.171428572 = -2.210549844 Simplifying x + 2.171428572 = -2.210549844 Reorder the terms: 2.171428572 + x = -2.210549844 Solving 2.171428572 + x = -2.210549844 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.171428572' to each side of the equation. 2.171428572 + -2.171428572 + x = -2.210549844 + -2.171428572 Combine like terms: 2.171428572 + -2.171428572 = 0.000000000 0.000000000 + x = -2.210549844 + -2.171428572 x = -2.210549844 + -2.171428572 Combine like terms: -2.210549844 + -2.171428572 = -4.381978416 x = -4.381978416 Simplifying x = -4.381978416Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.039121272, -4.381978416}
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