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Simplifying 9x2 + 30x = 10 Reorder the terms: 30x + 9x2 = 10 Solving 30x + 9x2 = 10 Solving for variable 'x'. Reorder the terms: -10 + 30x + 9x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + 30x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.111111111 + 3.333333333x + x2 = 0 Move the constant term to the right: Add '1.111111111' to each side of the equation. -1.111111111 + 3.333333333x + 1.111111111 + x2 = 0 + 1.111111111 Reorder the terms: -1.111111111 + 1.111111111 + 3.333333333x + x2 = 0 + 1.111111111 Combine like terms: -1.111111111 + 1.111111111 = 0.000000000 0.000000000 + 3.333333333x + x2 = 0 + 1.111111111 3.333333333x + x2 = 0 + 1.111111111 Combine like terms: 0 + 1.111111111 = 1.111111111 3.333333333x + x2 = 1.111111111 The x term is 3.333333333x. Take half its coefficient (1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. 3.333333333x + 2.777777779 + x2 = 1.111111111 + 2.777777779 Reorder the terms: 2.777777779 + 3.333333333x + x2 = 1.111111111 + 2.777777779 Combine like terms: 1.111111111 + 2.777777779 = 3.88888889 2.777777779 + 3.333333333x + x2 = 3.88888889 Factor a perfect square on the left side: (x + 1.666666667)(x + 1.666666667) = 3.88888889 Calculate the square root of the right side: 1.972026595 Break this problem into two subproblems by setting (x + 1.666666667) equal to 1.972026595 and -1.972026595.Subproblem 1
x + 1.666666667 = 1.972026595 Simplifying x + 1.666666667 = 1.972026595 Reorder the terms: 1.666666667 + x = 1.972026595 Solving 1.666666667 + x = 1.972026595 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + x = 1.972026595 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = 1.972026595 + -1.666666667 x = 1.972026595 + -1.666666667 Combine like terms: 1.972026595 + -1.666666667 = 0.305359928 x = 0.305359928 Simplifying x = 0.305359928Subproblem 2
x + 1.666666667 = -1.972026595 Simplifying x + 1.666666667 = -1.972026595 Reorder the terms: 1.666666667 + x = -1.972026595 Solving 1.666666667 + x = -1.972026595 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + x = -1.972026595 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = -1.972026595 + -1.666666667 x = -1.972026595 + -1.666666667 Combine like terms: -1.972026595 + -1.666666667 = -3.638693262 x = -3.638693262 Simplifying x = -3.638693262Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.305359928, -3.638693262}
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