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Simplifying 32x2 + -70x + -3 = 0 Reorder the terms: -3 + -70x + 32x2 = 0 Solving -3 + -70x + 32x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. -0.09375 + -2.1875x + x2 = 0 Move the constant term to the right: Add '0.09375' to each side of the equation. -0.09375 + -2.1875x + 0.09375 + x2 = 0 + 0.09375 Reorder the terms: -0.09375 + 0.09375 + -2.1875x + x2 = 0 + 0.09375 Combine like terms: -0.09375 + 0.09375 = 0.00000 0.00000 + -2.1875x + x2 = 0 + 0.09375 -2.1875x + x2 = 0 + 0.09375 Combine like terms: 0 + 0.09375 = 0.09375 -2.1875x + x2 = 0.09375 The x term is -2.1875x. Take half its coefficient (-1.09375). Square it (1.196289063) and add it to both sides. Add '1.196289063' to each side of the equation. -2.1875x + 1.196289063 + x2 = 0.09375 + 1.196289063 Reorder the terms: 1.196289063 + -2.1875x + x2 = 0.09375 + 1.196289063 Combine like terms: 0.09375 + 1.196289063 = 1.290039063 1.196289063 + -2.1875x + x2 = 1.290039063 Factor a perfect square on the left side: (x + -1.09375)(x + -1.09375) = 1.290039063 Calculate the square root of the right side: 1.135798866 Break this problem into two subproblems by setting (x + -1.09375) equal to 1.135798866 and -1.135798866.Subproblem 1
x + -1.09375 = 1.135798866 Simplifying x + -1.09375 = 1.135798866 Reorder the terms: -1.09375 + x = 1.135798866 Solving -1.09375 + x = 1.135798866 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.09375' to each side of the equation. -1.09375 + 1.09375 + x = 1.135798866 + 1.09375 Combine like terms: -1.09375 + 1.09375 = 0.00000 0.00000 + x = 1.135798866 + 1.09375 x = 1.135798866 + 1.09375 Combine like terms: 1.135798866 + 1.09375 = 2.229548866 x = 2.229548866 Simplifying x = 2.229548866Subproblem 2
x + -1.09375 = -1.135798866 Simplifying x + -1.09375 = -1.135798866 Reorder the terms: -1.09375 + x = -1.135798866 Solving -1.09375 + x = -1.135798866 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.09375' to each side of the equation. -1.09375 + 1.09375 + x = -1.135798866 + 1.09375 Combine like terms: -1.09375 + 1.09375 = 0.00000 0.00000 + x = -1.135798866 + 1.09375 x = -1.135798866 + 1.09375 Combine like terms: -1.135798866 + 1.09375 = -0.042048866 x = -0.042048866 Simplifying x = -0.042048866Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.229548866, -0.042048866}
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