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Simplifying 9x2 + -24x + 16 = 10x Reorder the terms: 16 + -24x + 9x2 = 10x Solving 16 + -24x + 9x2 = 10x Solving for variable 'x'. Reorder the terms: 16 + -24x + -10x + 9x2 = 10x + -10x Combine like terms: -24x + -10x = -34x 16 + -34x + 9x2 = 10x + -10x Combine like terms: 10x + -10x = 0 16 + -34x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 1.777777778 + -3.777777778x + x2 = 0 Move the constant term to the right: Add '-1.777777778' to each side of the equation. 1.777777778 + -3.777777778x + -1.777777778 + x2 = 0 + -1.777777778 Reorder the terms: 1.777777778 + -1.777777778 + -3.777777778x + x2 = 0 + -1.777777778 Combine like terms: 1.777777778 + -1.777777778 = 0.000000000 0.000000000 + -3.777777778x + x2 = 0 + -1.777777778 -3.777777778x + x2 = 0 + -1.777777778 Combine like terms: 0 + -1.777777778 = -1.777777778 -3.777777778x + x2 = -1.777777778 The x term is -3.777777778x. Take half its coefficient (-1.888888889). Square it (3.567901235) and add it to both sides. Add '3.567901235' to each side of the equation. -3.777777778x + 3.567901235 + x2 = -1.777777778 + 3.567901235 Reorder the terms: 3.567901235 + -3.777777778x + x2 = -1.777777778 + 3.567901235 Combine like terms: -1.777777778 + 3.567901235 = 1.790123457 3.567901235 + -3.777777778x + x2 = 1.790123457 Factor a perfect square on the left side: (x + -1.888888889)(x + -1.888888889) = 1.790123457 Calculate the square root of the right side: 1.337954953 Break this problem into two subproblems by setting (x + -1.888888889) equal to 1.337954953 and -1.337954953.Subproblem 1
x + -1.888888889 = 1.337954953 Simplifying x + -1.888888889 = 1.337954953 Reorder the terms: -1.888888889 + x = 1.337954953 Solving -1.888888889 + x = 1.337954953 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.888888889' to each side of the equation. -1.888888889 + 1.888888889 + x = 1.337954953 + 1.888888889 Combine like terms: -1.888888889 + 1.888888889 = 0.000000000 0.000000000 + x = 1.337954953 + 1.888888889 x = 1.337954953 + 1.888888889 Combine like terms: 1.337954953 + 1.888888889 = 3.226843842 x = 3.226843842 Simplifying x = 3.226843842Subproblem 2
x + -1.888888889 = -1.337954953 Simplifying x + -1.888888889 = -1.337954953 Reorder the terms: -1.888888889 + x = -1.337954953 Solving -1.888888889 + x = -1.337954953 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.888888889' to each side of the equation. -1.888888889 + 1.888888889 + x = -1.337954953 + 1.888888889 Combine like terms: -1.888888889 + 1.888888889 = 0.000000000 0.000000000 + x = -1.337954953 + 1.888888889 x = -1.337954953 + 1.888888889 Combine like terms: -1.337954953 + 1.888888889 = 0.550933936 x = 0.550933936 Simplifying x = 0.550933936Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.226843842, 0.550933936}
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