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Simplifying 15x(3x + -5) = -2 Reorder the terms: 15x(-5 + 3x) = -2 (-5 * 15x + 3x * 15x) = -2 (-75x + 45x2) = -2 Solving -75x + 45x2 = -2 Solving for variable 'x'. Reorder the terms: 2 + -75x + 45x2 = -2 + 2 Combine like terms: -2 + 2 = 0 2 + -75x + 45x2 = 0 Begin completing the square. Divide all terms by 45 the coefficient of the squared term: Divide each side by '45'. 0.04444444444 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '-0.04444444444' to each side of the equation. 0.04444444444 + -1.666666667x + -0.04444444444 + x2 = 0 + -0.04444444444 Reorder the terms: 0.04444444444 + -0.04444444444 + -1.666666667x + x2 = 0 + -0.04444444444 Combine like terms: 0.04444444444 + -0.04444444444 = 0.00000000000 0.00000000000 + -1.666666667x + x2 = 0 + -0.04444444444 -1.666666667x + x2 = 0 + -0.04444444444 Combine like terms: 0 + -0.04444444444 = -0.04444444444 -1.666666667x + x2 = -0.04444444444 The x term is -1.666666667x. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667x + 0.6944444447 + x2 = -0.04444444444 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = -0.04444444444 + 0.6944444447 Combine like terms: -0.04444444444 + 0.6944444447 = 0.65000000026 0.6944444447 + -1.666666667x + x2 = 0.65000000026 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = 0.65000000026 Calculate the square root of the right side: 0.806225775 Break this problem into two subproblems by setting (x + -0.8333333335) equal to 0.806225775 and -0.806225775.Subproblem 1
x + -0.8333333335 = 0.806225775 Simplifying x + -0.8333333335 = 0.806225775 Reorder the terms: -0.8333333335 + x = 0.806225775 Solving -0.8333333335 + x = 0.806225775 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = 0.806225775 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 0.806225775 + 0.8333333335 x = 0.806225775 + 0.8333333335 Combine like terms: 0.806225775 + 0.8333333335 = 1.6395591085 x = 1.6395591085 Simplifying x = 1.6395591085Subproblem 2
x + -0.8333333335 = -0.806225775 Simplifying x + -0.8333333335 = -0.806225775 Reorder the terms: -0.8333333335 + x = -0.806225775 Solving -0.8333333335 + x = -0.806225775 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = -0.806225775 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -0.806225775 + 0.8333333335 x = -0.806225775 + 0.8333333335 Combine like terms: -0.806225775 + 0.8333333335 = 0.0271075585 x = 0.0271075585 Simplifying x = 0.0271075585Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6395591085, 0.0271075585}
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