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Simplifying 9x2 + 30x + 25 = 12 Reorder the terms: 25 + 30x + 9x2 = 12 Solving 25 + 30x + 9x2 = 12 Solving for variable 'x'. Reorder the terms: 25 + -12 + 30x + 9x2 = 12 + -12 Combine like terms: 25 + -12 = 13 13 + 30x + 9x2 = 12 + -12 Combine like terms: 12 + -12 = 0 13 + 30x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 1.444444444 + 3.333333333x + x2 = 0 Move the constant term to the right: Add '-1.444444444' to each side of the equation. 1.444444444 + 3.333333333x + -1.444444444 + x2 = 0 + -1.444444444 Reorder the terms: 1.444444444 + -1.444444444 + 3.333333333x + x2 = 0 + -1.444444444 Combine like terms: 1.444444444 + -1.444444444 = 0.000000000 0.000000000 + 3.333333333x + x2 = 0 + -1.444444444 3.333333333x + x2 = 0 + -1.444444444 Combine like terms: 0 + -1.444444444 = -1.444444444 3.333333333x + x2 = -1.444444444 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 = -1.444444444 + 2.777777779 Reorder the terms: 2.777777779 + 3.333333333x + x2 = -1.444444444 + 2.777777779 Combine like terms: -1.444444444 + 2.777777779 = 1.333333335 2.777777779 + 3.333333333x + x2 = 1.333333335 Factor a perfect square on the left side: (x + 1.666666667)(x + 1.666666667) = 1.333333335 Calculate the square root of the right side: 1.154700539 Break this problem into two subproblems by setting (x + 1.666666667) equal to 1.154700539 and -1.154700539.Subproblem 1
x + 1.666666667 = 1.154700539 Simplifying x + 1.666666667 = 1.154700539 Reorder the terms: 1.666666667 + x = 1.154700539 Solving 1.666666667 + x = 1.154700539 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 = 1.154700539 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = 1.154700539 + -1.666666667 x = 1.154700539 + -1.666666667 Combine like terms: 1.154700539 + -1.666666667 = -0.511966128 x = -0.511966128 Simplifying x = -0.511966128Subproblem 2
x + 1.666666667 = -1.154700539 Simplifying x + 1.666666667 = -1.154700539 Reorder the terms: 1.666666667 + x = -1.154700539 Solving 1.666666667 + x = -1.154700539 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 = -1.154700539 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = -1.154700539 + -1.666666667 x = -1.154700539 + -1.666666667 Combine like terms: -1.154700539 + -1.666666667 = -2.821367206 x = -2.821367206 Simplifying x = -2.821367206Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.511966128, -2.821367206}
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