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Simplifying 75x2 + 16x + -6 = 0 Reorder the terms: -6 + 16x + 75x2 = 0 Solving -6 + 16x + 75x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 75 the coefficient of the squared term: Divide each side by '75'. -0.08 + 0.2133333333x + x2 = 0 Move the constant term to the right: Add '0.08' to each side of the equation. -0.08 + 0.2133333333x + 0.08 + x2 = 0 + 0.08 Reorder the terms: -0.08 + 0.08 + 0.2133333333x + x2 = 0 + 0.08 Combine like terms: -0.08 + 0.08 = 0.00 0.00 + 0.2133333333x + x2 = 0 + 0.08 0.2133333333x + x2 = 0 + 0.08 Combine like terms: 0 + 0.08 = 0.08 0.2133333333x + x2 = 0.08 The x term is 0.2133333333x. Take half its coefficient (0.1066666667). Square it (0.01137777778) and add it to both sides. Add '0.01137777778' to each side of the equation. 0.2133333333x + 0.01137777778 + x2 = 0.08 + 0.01137777778 Reorder the terms: 0.01137777778 + 0.2133333333x + x2 = 0.08 + 0.01137777778 Combine like terms: 0.08 + 0.01137777778 = 0.09137777778 0.01137777778 + 0.2133333333x + x2 = 0.09137777778 Factor a perfect square on the left side: (x + 0.1066666667)(x + 0.1066666667) = 0.09137777778 Calculate the square root of the right side: 0.302287575 Break this problem into two subproblems by setting (x + 0.1066666667) equal to 0.302287575 and -0.302287575.Subproblem 1
x + 0.1066666667 = 0.302287575 Simplifying x + 0.1066666667 = 0.302287575 Reorder the terms: 0.1066666667 + x = 0.302287575 Solving 0.1066666667 + x = 0.302287575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1066666667' to each side of the equation. 0.1066666667 + -0.1066666667 + x = 0.302287575 + -0.1066666667 Combine like terms: 0.1066666667 + -0.1066666667 = 0.0000000000 0.0000000000 + x = 0.302287575 + -0.1066666667 x = 0.302287575 + -0.1066666667 Combine like terms: 0.302287575 + -0.1066666667 = 0.1956209083 x = 0.1956209083 Simplifying x = 0.1956209083Subproblem 2
x + 0.1066666667 = -0.302287575 Simplifying x + 0.1066666667 = -0.302287575 Reorder the terms: 0.1066666667 + x = -0.302287575 Solving 0.1066666667 + x = -0.302287575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1066666667' to each side of the equation. 0.1066666667 + -0.1066666667 + x = -0.302287575 + -0.1066666667 Combine like terms: 0.1066666667 + -0.1066666667 = 0.0000000000 0.0000000000 + x = -0.302287575 + -0.1066666667 x = -0.302287575 + -0.1066666667 Combine like terms: -0.302287575 + -0.1066666667 = -0.4089542417 x = -0.4089542417 Simplifying x = -0.4089542417Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1956209083, -0.4089542417}
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