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Simplifying 9x2 + 16x + 64 = 88 Reorder the terms: 64 + 16x + 9x2 = 88 Solving 64 + 16x + 9x2 = 88 Solving for variable 'x'. Reorder the terms: 64 + -88 + 16x + 9x2 = 88 + -88 Combine like terms: 64 + -88 = -24 -24 + 16x + 9x2 = 88 + -88 Combine like terms: 88 + -88 = 0 -24 + 16x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2.666666667 + 1.777777778x + x2 = 0 Move the constant term to the right: Add '2.666666667' to each side of the equation. -2.666666667 + 1.777777778x + 2.666666667 + x2 = 0 + 2.666666667 Reorder the terms: -2.666666667 + 2.666666667 + 1.777777778x + x2 = 0 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + 1.777777778x + x2 = 0 + 2.666666667 1.777777778x + x2 = 0 + 2.666666667 Combine like terms: 0 + 2.666666667 = 2.666666667 1.777777778x + x2 = 2.666666667 The x term is 1.777777778x. Take half its coefficient (0.888888889). Square it (0.7901234570) and add it to both sides. Add '0.7901234570' to each side of the equation. 1.777777778x + 0.7901234570 + x2 = 2.666666667 + 0.7901234570 Reorder the terms: 0.7901234570 + 1.777777778x + x2 = 2.666666667 + 0.7901234570 Combine like terms: 2.666666667 + 0.7901234570 = 3.456790124 0.7901234570 + 1.777777778x + x2 = 3.456790124 Factor a perfect square on the left side: (x + 0.888888889)(x + 0.888888889) = 3.456790124 Calculate the square root of the right side: 1.859244504 Break this problem into two subproblems by setting (x + 0.888888889) equal to 1.859244504 and -1.859244504.Subproblem 1
x + 0.888888889 = 1.859244504 Simplifying x + 0.888888889 = 1.859244504 Reorder the terms: 0.888888889 + x = 1.859244504 Solving 0.888888889 + x = 1.859244504 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.888888889' to each side of the equation. 0.888888889 + -0.888888889 + x = 1.859244504 + -0.888888889 Combine like terms: 0.888888889 + -0.888888889 = 0.000000000 0.000000000 + x = 1.859244504 + -0.888888889 x = 1.859244504 + -0.888888889 Combine like terms: 1.859244504 + -0.888888889 = 0.970355615 x = 0.970355615 Simplifying x = 0.970355615Subproblem 2
x + 0.888888889 = -1.859244504 Simplifying x + 0.888888889 = -1.859244504 Reorder the terms: 0.888888889 + x = -1.859244504 Solving 0.888888889 + x = -1.859244504 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.888888889' to each side of the equation. 0.888888889 + -0.888888889 + x = -1.859244504 + -0.888888889 Combine like terms: 0.888888889 + -0.888888889 = 0.000000000 0.000000000 + x = -1.859244504 + -0.888888889 x = -1.859244504 + -0.888888889 Combine like terms: -1.859244504 + -0.888888889 = -2.748133393 x = -2.748133393 Simplifying x = -2.748133393Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.970355615, -2.748133393}
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