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Simplifying 72x2 + 95x = 100 Reorder the terms: 95x + 72x2 = 100 Solving 95x + 72x2 = 100 Solving for variable 'x'. Reorder the terms: -100 + 95x + 72x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -100 + 95x + 72x2 = 0 Begin completing the square. Divide all terms by 72 the coefficient of the squared term: Divide each side by '72'. -1.388888889 + 1.319444444x + x2 = 0 Move the constant term to the right: Add '1.388888889' to each side of the equation. -1.388888889 + 1.319444444x + 1.388888889 + x2 = 0 + 1.388888889 Reorder the terms: -1.388888889 + 1.388888889 + 1.319444444x + x2 = 0 + 1.388888889 Combine like terms: -1.388888889 + 1.388888889 = 0.000000000 0.000000000 + 1.319444444x + x2 = 0 + 1.388888889 1.319444444x + x2 = 0 + 1.388888889 Combine like terms: 0 + 1.388888889 = 1.388888889 1.319444444x + x2 = 1.388888889 The x term is 1.319444444x. Take half its coefficient (0.659722222). Square it (0.4352334102) and add it to both sides. Add '0.4352334102' to each side of the equation. 1.319444444x + 0.4352334102 + x2 = 1.388888889 + 0.4352334102 Reorder the terms: 0.4352334102 + 1.319444444x + x2 = 1.388888889 + 0.4352334102 Combine like terms: 1.388888889 + 0.4352334102 = 1.8241222992 0.4352334102 + 1.319444444x + x2 = 1.8241222992 Factor a perfect square on the left side: (x + 0.659722222)(x + 0.659722222) = 1.8241222992 Calculate the square root of the right side: 1.350600718 Break this problem into two subproblems by setting (x + 0.659722222) equal to 1.350600718 and -1.350600718.Subproblem 1
x + 0.659722222 = 1.350600718 Simplifying x + 0.659722222 = 1.350600718 Reorder the terms: 0.659722222 + x = 1.350600718 Solving 0.659722222 + x = 1.350600718 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.659722222' to each side of the equation. 0.659722222 + -0.659722222 + x = 1.350600718 + -0.659722222 Combine like terms: 0.659722222 + -0.659722222 = 0.000000000 0.000000000 + x = 1.350600718 + -0.659722222 x = 1.350600718 + -0.659722222 Combine like terms: 1.350600718 + -0.659722222 = 0.690878496 x = 0.690878496 Simplifying x = 0.690878496Subproblem 2
x + 0.659722222 = -1.350600718 Simplifying x + 0.659722222 = -1.350600718 Reorder the terms: 0.659722222 + x = -1.350600718 Solving 0.659722222 + x = -1.350600718 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.659722222' to each side of the equation. 0.659722222 + -0.659722222 + x = -1.350600718 + -0.659722222 Combine like terms: 0.659722222 + -0.659722222 = 0.000000000 0.000000000 + x = -1.350600718 + -0.659722222 x = -1.350600718 + -0.659722222 Combine like terms: -1.350600718 + -0.659722222 = -2.01032294 x = -2.01032294 Simplifying x = -2.01032294Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.690878496, -2.01032294}
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