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Simplifying (5x + 7)(5x + 7) = 12 Reorder the terms: (7 + 5x)(5x + 7) = 12 Reorder the terms: (7 + 5x)(7 + 5x) = 12 Multiply (7 + 5x) * (7 + 5x) (7(7 + 5x) + 5x * (7 + 5x)) = 12 ((7 * 7 + 5x * 7) + 5x * (7 + 5x)) = 12 ((49 + 35x) + 5x * (7 + 5x)) = 12 (49 + 35x + (7 * 5x + 5x * 5x)) = 12 (49 + 35x + (35x + 25x2)) = 12 Combine like terms: 35x + 35x = 70x (49 + 70x + 25x2) = 12 Solving 49 + 70x + 25x2 = 12 Solving for variable 'x'. Reorder the terms: 49 + -12 + 70x + 25x2 = 12 + -12 Combine like terms: 49 + -12 = 37 37 + 70x + 25x2 = 12 + -12 Combine like terms: 12 + -12 = 0 37 + 70x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 1.48 + 2.8x + x2 = 0 Move the constant term to the right: Add '-1.48' to each side of the equation. 1.48 + 2.8x + -1.48 + x2 = 0 + -1.48 Reorder the terms: 1.48 + -1.48 + 2.8x + x2 = 0 + -1.48 Combine like terms: 1.48 + -1.48 = 0.00 0.00 + 2.8x + x2 = 0 + -1.48 2.8x + x2 = 0 + -1.48 Combine like terms: 0 + -1.48 = -1.48 2.8x + x2 = -1.48 The x term is 2.8x. Take half its coefficient (1.4). Square it (1.96) and add it to both sides. Add '1.96' to each side of the equation. 2.8x + 1.96 + x2 = -1.48 + 1.96 Reorder the terms: 1.96 + 2.8x + x2 = -1.48 + 1.96 Combine like terms: -1.48 + 1.96 = 0.48 1.96 + 2.8x + x2 = 0.48 Factor a perfect square on the left side: (x + 1.4)(x + 1.4) = 0.48 Calculate the square root of the right side: 0.692820323 Break this problem into two subproblems by setting (x + 1.4) equal to 0.692820323 and -0.692820323.Subproblem 1
x + 1.4 = 0.692820323 Simplifying x + 1.4 = 0.692820323 Reorder the terms: 1.4 + x = 0.692820323 Solving 1.4 + x = 0.692820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.4' to each side of the equation. 1.4 + -1.4 + x = 0.692820323 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + x = 0.692820323 + -1.4 x = 0.692820323 + -1.4 Combine like terms: 0.692820323 + -1.4 = -0.707179677 x = -0.707179677 Simplifying x = -0.707179677Subproblem 2
x + 1.4 = -0.692820323 Simplifying x + 1.4 = -0.692820323 Reorder the terms: 1.4 + x = -0.692820323 Solving 1.4 + x = -0.692820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.4' to each side of the equation. 1.4 + -1.4 + x = -0.692820323 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + x = -0.692820323 + -1.4 x = -0.692820323 + -1.4 Combine like terms: -0.692820323 + -1.4 = -2.092820323 x = -2.092820323 Simplifying x = -2.092820323Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.707179677, -2.092820323}
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