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Simplifying 3 + 10x(6 + 5x) = 7x + 16 + -3x 3 + (6 * 10x + 5x * 10x) = 7x + 16 + -3x 3 + (60x + 50x2) = 7x + 16 + -3x Reorder the terms: 3 + 60x + 50x2 = 16 + 7x + -3x Combine like terms: 7x + -3x = 4x 3 + 60x + 50x2 = 16 + 4x Solving 3 + 60x + 50x2 = 16 + 4x Solving for variable 'x'. Reorder the terms: 3 + -16 + 60x + -4x + 50x2 = 16 + 4x + -16 + -4x Combine like terms: 3 + -16 = -13 -13 + 60x + -4x + 50x2 = 16 + 4x + -16 + -4x Combine like terms: 60x + -4x = 56x -13 + 56x + 50x2 = 16 + 4x + -16 + -4x Reorder the terms: -13 + 56x + 50x2 = 16 + -16 + 4x + -4x Combine like terms: 16 + -16 = 0 -13 + 56x + 50x2 = 0 + 4x + -4x -13 + 56x + 50x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -13 + 56x + 50x2 = 0 Begin completing the square. Divide all terms by 50 the coefficient of the squared term: Divide each side by '50'. -0.26 + 1.12x + x2 = 0.0 Move the constant term to the right: Add '0.26' to each side of the equation. -0.26 + 1.12x + 0.26 + x2 = 0.0 + 0.26 Reorder the terms: -0.26 + 0.26 + 1.12x + x2 = 0.0 + 0.26 Combine like terms: -0.26 + 0.26 = 0.00 0.00 + 1.12x + x2 = 0.0 + 0.26 1.12x + x2 = 0.0 + 0.26 Combine like terms: 0.0 + 0.26 = 0.26 1.12x + x2 = 0.26 The x term is 1.12x. Take half its coefficient (0.56). Square it (0.3136) and add it to both sides. Add '0.3136' to each side of the equation. 1.12x + 0.3136 + x2 = 0.26 + 0.3136 Reorder the terms: 0.3136 + 1.12x + x2 = 0.26 + 0.3136 Combine like terms: 0.26 + 0.3136 = 0.5736 0.3136 + 1.12x + x2 = 0.5736 Factor a perfect square on the left side: (x + 0.56)(x + 0.56) = 0.5736 Calculate the square root of the right side: 0.757363849 Break this problem into two subproblems by setting (x + 0.56) equal to 0.757363849 and -0.757363849.Subproblem 1
x + 0.56 = 0.757363849 Simplifying x + 0.56 = 0.757363849 Reorder the terms: 0.56 + x = 0.757363849 Solving 0.56 + x = 0.757363849 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.56' to each side of the equation. 0.56 + -0.56 + x = 0.757363849 + -0.56 Combine like terms: 0.56 + -0.56 = 0.00 0.00 + x = 0.757363849 + -0.56 x = 0.757363849 + -0.56 Combine like terms: 0.757363849 + -0.56 = 0.197363849 x = 0.197363849 Simplifying x = 0.197363849Subproblem 2
x + 0.56 = -0.757363849 Simplifying x + 0.56 = -0.757363849 Reorder the terms: 0.56 + x = -0.757363849 Solving 0.56 + x = -0.757363849 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.56' to each side of the equation. 0.56 + -0.56 + x = -0.757363849 + -0.56 Combine like terms: 0.56 + -0.56 = 0.00 0.00 + x = -0.757363849 + -0.56 x = -0.757363849 + -0.56 Combine like terms: -0.757363849 + -0.56 = -1.317363849 x = -1.317363849 Simplifying x = -1.317363849Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.197363849, -1.317363849}
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