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Simplifying 5x(9x + -3) = 4 Reorder the terms: 5x(-3 + 9x) = 4 (-3 * 5x + 9x * 5x) = 4 (-15x + 45x2) = 4 Solving -15x + 45x2 = 4 Solving for variable 'x'. Reorder the terms: -4 + -15x + 45x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + -15x + 45x2 = 0 Begin completing the square. Divide all terms by 45 the coefficient of the squared term: Divide each side by '45'. -0.08888888889 + -0.3333333333x + x2 = 0 Move the constant term to the right: Add '0.08888888889' to each side of the equation. -0.08888888889 + -0.3333333333x + 0.08888888889 + x2 = 0 + 0.08888888889 Reorder the terms: -0.08888888889 + 0.08888888889 + -0.3333333333x + x2 = 0 + 0.08888888889 Combine like terms: -0.08888888889 + 0.08888888889 = 0.00000000000 0.00000000000 + -0.3333333333x + x2 = 0 + 0.08888888889 -0.3333333333x + x2 = 0 + 0.08888888889 Combine like terms: 0 + 0.08888888889 = 0.08888888889 -0.3333333333x + x2 = 0.08888888889 The x term is -0.3333333333x. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333x + 0.02777777779 + x2 = 0.08888888889 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333x + x2 = 0.08888888889 + 0.02777777779 Combine like terms: 0.08888888889 + 0.02777777779 = 0.11666666668 0.02777777779 + -0.3333333333x + x2 = 0.11666666668 Factor a perfect square on the left side: (x + -0.1666666667)(x + -0.1666666667) = 0.11666666668 Calculate the square root of the right side: 0.341565026 Break this problem into two subproblems by setting (x + -0.1666666667) equal to 0.341565026 and -0.341565026.Subproblem 1
x + -0.1666666667 = 0.341565026 Simplifying x + -0.1666666667 = 0.341565026 Reorder the terms: -0.1666666667 + x = 0.341565026 Solving -0.1666666667 + x = 0.341565026 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = 0.341565026 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = 0.341565026 + 0.1666666667 x = 0.341565026 + 0.1666666667 Combine like terms: 0.341565026 + 0.1666666667 = 0.5082316927 x = 0.5082316927 Simplifying x = 0.5082316927Subproblem 2
x + -0.1666666667 = -0.341565026 Simplifying x + -0.1666666667 = -0.341565026 Reorder the terms: -0.1666666667 + x = -0.341565026 Solving -0.1666666667 + x = -0.341565026 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = -0.341565026 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = -0.341565026 + 0.1666666667 x = -0.341565026 + 0.1666666667 Combine like terms: -0.341565026 + 0.1666666667 = -0.1748983593 x = -0.1748983593 Simplifying x = -0.1748983593Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5082316927, -0.1748983593}
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