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Simplifying -6x2 + 5x + 6 = 7.01466 Reorder the terms: 6 + 5x + -6x2 = 7.01466 Solving 6 + 5x + -6x2 = 7.01466 Solving for variable 'x'. Reorder the terms: 6 + -7.01466 + 5x + -6x2 = 7.01466 + -7.01466 Combine like terms: 6 + -7.01466 = -1.01466 -1.01466 + 5x + -6x2 = 7.01466 + -7.01466 Combine like terms: 7.01466 + -7.01466 = 0.00000 -1.01466 + 5x + -6x2 = 0.00000 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. 0.16911 + -0.8333333333x + x2 = 0.00000 Move the constant term to the right: Add '-0.16911' to each side of the equation. 0.16911 + -0.8333333333x + -0.16911 + x2 = 0.00000 + -0.16911 Reorder the terms: 0.16911 + -0.16911 + -0.8333333333x + x2 = 0.00000 + -0.16911 Combine like terms: 0.16911 + -0.16911 = 0.00000 0.00000 + -0.8333333333x + x2 = 0.00000 + -0.16911 -0.8333333333x + x2 = 0.00000 + -0.16911 Combine like terms: 0.00000 + -0.16911 = -0.16911 -0.8333333333x + x2 = -0.16911 The x term is -0.8333333333x. Take half its coefficient (-0.4166666667). Square it (0.1736111111) and add it to both sides. Add '0.1736111111' to each side of the equation. -0.8333333333x + 0.1736111111 + x2 = -0.16911 + 0.1736111111 Reorder the terms: 0.1736111111 + -0.8333333333x + x2 = -0.16911 + 0.1736111111 Combine like terms: -0.16911 + 0.1736111111 = 0.0045011111 0.1736111111 + -0.8333333333x + x2 = 0.0045011111 Factor a perfect square on the left side: (x + -0.4166666667)(x + -0.4166666667) = 0.0045011111 Calculate the square root of the right side: 0.06709032 Break this problem into two subproblems by setting (x + -0.4166666667) equal to 0.06709032 and -0.06709032.Subproblem 1
x + -0.4166666667 = 0.06709032 Simplifying x + -0.4166666667 = 0.06709032 Reorder the terms: -0.4166666667 + x = 0.06709032 Solving -0.4166666667 + x = 0.06709032 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4166666667' to each side of the equation. -0.4166666667 + 0.4166666667 + x = 0.06709032 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + x = 0.06709032 + 0.4166666667 x = 0.06709032 + 0.4166666667 Combine like terms: 0.06709032 + 0.4166666667 = 0.4837569867 x = 0.4837569867 Simplifying x = 0.4837569867Subproblem 2
x + -0.4166666667 = -0.06709032 Simplifying x + -0.4166666667 = -0.06709032 Reorder the terms: -0.4166666667 + x = -0.06709032 Solving -0.4166666667 + x = -0.06709032 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4166666667' to each side of the equation. -0.4166666667 + 0.4166666667 + x = -0.06709032 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + x = -0.06709032 + 0.4166666667 x = -0.06709032 + 0.4166666667 Combine like terms: -0.06709032 + 0.4166666667 = 0.3495763467 x = 0.3495763467 Simplifying x = 0.3495763467Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4837569867, 0.3495763467}
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