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Simplifying 9x2 + 43x + -3 = 0 Reorder the terms: -3 + 43x + 9x2 = 0 Solving -3 + 43x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.3333333333 + 4.777777778x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + 4.777777778x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + 4.777777778x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + 4.777777778x + x2 = 0 + 0.3333333333 4.777777778x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 4.777777778x + x2 = 0.3333333333 The x term is 4.777777778x. Take half its coefficient (2.388888889). Square it (5.706790124) and add it to both sides. Add '5.706790124' to each side of the equation. 4.777777778x + 5.706790124 + x2 = 0.3333333333 + 5.706790124 Reorder the terms: 5.706790124 + 4.777777778x + x2 = 0.3333333333 + 5.706790124 Combine like terms: 0.3333333333 + 5.706790124 = 6.0401234573 5.706790124 + 4.777777778x + x2 = 6.0401234573 Factor a perfect square on the left side: (x + 2.388888889)(x + 2.388888889) = 6.0401234573 Calculate the square root of the right side: 2.457666262 Break this problem into two subproblems by setting (x + 2.388888889) equal to 2.457666262 and -2.457666262.Subproblem 1
x + 2.388888889 = 2.457666262 Simplifying x + 2.388888889 = 2.457666262 Reorder the terms: 2.388888889 + x = 2.457666262 Solving 2.388888889 + x = 2.457666262 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.388888889' to each side of the equation. 2.388888889 + -2.388888889 + x = 2.457666262 + -2.388888889 Combine like terms: 2.388888889 + -2.388888889 = 0.000000000 0.000000000 + x = 2.457666262 + -2.388888889 x = 2.457666262 + -2.388888889 Combine like terms: 2.457666262 + -2.388888889 = 0.068777373 x = 0.068777373 Simplifying x = 0.068777373Subproblem 2
x + 2.388888889 = -2.457666262 Simplifying x + 2.388888889 = -2.457666262 Reorder the terms: 2.388888889 + x = -2.457666262 Solving 2.388888889 + x = -2.457666262 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.388888889' to each side of the equation. 2.388888889 + -2.388888889 + x = -2.457666262 + -2.388888889 Combine like terms: 2.388888889 + -2.388888889 = 0.000000000 0.000000000 + x = -2.457666262 + -2.388888889 x = -2.457666262 + -2.388888889 Combine like terms: -2.457666262 + -2.388888889 = -4.846555151 x = -4.846555151 Simplifying x = -4.846555151Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.068777373, -4.846555151}
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