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Simplifying x(5x + 11) = 2x2 + 10 Reorder the terms: x(11 + 5x) = 2x2 + 10 (11 * x + 5x * x) = 2x2 + 10 (11x + 5x2) = 2x2 + 10 Reorder the terms: 11x + 5x2 = 10 + 2x2 Solving 11x + 5x2 = 10 + 2x2 Solving for variable 'x'. Reorder the terms: -10 + 11x + 5x2 + -2x2 = 10 + 2x2 + -10 + -2x2 Combine like terms: 5x2 + -2x2 = 3x2 -10 + 11x + 3x2 = 10 + 2x2 + -10 + -2x2 Reorder the terms: -10 + 11x + 3x2 = 10 + -10 + 2x2 + -2x2 Combine like terms: 10 + -10 = 0 -10 + 11x + 3x2 = 0 + 2x2 + -2x2 -10 + 11x + 3x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -10 + 11x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3.333333333 + 3.666666667x + x2 = 0 Move the constant term to the right: Add '3.333333333' to each side of the equation. -3.333333333 + 3.666666667x + 3.333333333 + x2 = 0 + 3.333333333 Reorder the terms: -3.333333333 + 3.333333333 + 3.666666667x + x2 = 0 + 3.333333333 Combine like terms: -3.333333333 + 3.333333333 = 0.000000000 0.000000000 + 3.666666667x + x2 = 0 + 3.333333333 3.666666667x + x2 = 0 + 3.333333333 Combine like terms: 0 + 3.333333333 = 3.333333333 3.666666667x + x2 = 3.333333333 The x term is 3.666666667x. Take half its coefficient (1.833333334). Square it (3.361111114) and add it to both sides. Add '3.361111114' to each side of the equation. 3.666666667x + 3.361111114 + x2 = 3.333333333 + 3.361111114 Reorder the terms: 3.361111114 + 3.666666667x + x2 = 3.333333333 + 3.361111114 Combine like terms: 3.333333333 + 3.361111114 = 6.694444447 3.361111114 + 3.666666667x + x2 = 6.694444447 Factor a perfect square on the left side: (x + 1.833333334)(x + 1.833333334) = 6.694444447 Calculate the square root of the right side: 2.58736245 Break this problem into two subproblems by setting (x + 1.833333334) equal to 2.58736245 and -2.58736245.Subproblem 1
x + 1.833333334 = 2.58736245 Simplifying x + 1.833333334 = 2.58736245 Reorder the terms: 1.833333334 + x = 2.58736245 Solving 1.833333334 + x = 2.58736245 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.833333334' to each side of the equation. 1.833333334 + -1.833333334 + x = 2.58736245 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + x = 2.58736245 + -1.833333334 x = 2.58736245 + -1.833333334 Combine like terms: 2.58736245 + -1.833333334 = 0.754029116 x = 0.754029116 Simplifying x = 0.754029116Subproblem 2
x + 1.833333334 = -2.58736245 Simplifying x + 1.833333334 = -2.58736245 Reorder the terms: 1.833333334 + x = -2.58736245 Solving 1.833333334 + x = -2.58736245 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.833333334' to each side of the equation. 1.833333334 + -1.833333334 + x = -2.58736245 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + x = -2.58736245 + -1.833333334 x = -2.58736245 + -1.833333334 Combine like terms: -2.58736245 + -1.833333334 = -4.420695784 x = -4.420695784 Simplifying x = -4.420695784Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.754029116, -4.420695784}
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