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Simplifying (5x + -2)(5 + 3x) = 7 Reorder the terms: (-2 + 5x)(5 + 3x) = 7 Multiply (-2 + 5x) * (5 + 3x) (-2(5 + 3x) + 5x * (5 + 3x)) = 7 ((5 * -2 + 3x * -2) + 5x * (5 + 3x)) = 7 ((-10 + -6x) + 5x * (5 + 3x)) = 7 (-10 + -6x + (5 * 5x + 3x * 5x)) = 7 (-10 + -6x + (25x + 15x2)) = 7 Combine like terms: -6x + 25x = 19x (-10 + 19x + 15x2) = 7 Solving -10 + 19x + 15x2 = 7 Solving for variable 'x'. Reorder the terms: -10 + -7 + 19x + 15x2 = 7 + -7 Combine like terms: -10 + -7 = -17 -17 + 19x + 15x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -17 + 19x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -1.133333333 + 1.266666667x + x2 = 0 Move the constant term to the right: Add '1.133333333' to each side of the equation. -1.133333333 + 1.266666667x + 1.133333333 + x2 = 0 + 1.133333333 Reorder the terms: -1.133333333 + 1.133333333 + 1.266666667x + x2 = 0 + 1.133333333 Combine like terms: -1.133333333 + 1.133333333 = 0.000000000 0.000000000 + 1.266666667x + x2 = 0 + 1.133333333 1.266666667x + x2 = 0 + 1.133333333 Combine like terms: 0 + 1.133333333 = 1.133333333 1.266666667x + x2 = 1.133333333 The x term is 1.266666667x. Take half its coefficient (0.6333333335). Square it (0.4011111113) and add it to both sides. Add '0.4011111113' to each side of the equation. 1.266666667x + 0.4011111113 + x2 = 1.133333333 + 0.4011111113 Reorder the terms: 0.4011111113 + 1.266666667x + x2 = 1.133333333 + 0.4011111113 Combine like terms: 1.133333333 + 0.4011111113 = 1.5344444443 0.4011111113 + 1.266666667x + x2 = 1.5344444443 Factor a perfect square on the left side: (x + 0.6333333335)(x + 0.6333333335) = 1.5344444443 Calculate the square root of the right side: 1.238726945 Break this problem into two subproblems by setting (x + 0.6333333335) equal to 1.238726945 and -1.238726945.Subproblem 1
x + 0.6333333335 = 1.238726945 Simplifying x + 0.6333333335 = 1.238726945 Reorder the terms: 0.6333333335 + x = 1.238726945 Solving 0.6333333335 + x = 1.238726945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6333333335' to each side of the equation. 0.6333333335 + -0.6333333335 + x = 1.238726945 + -0.6333333335 Combine like terms: 0.6333333335 + -0.6333333335 = 0.0000000000 0.0000000000 + x = 1.238726945 + -0.6333333335 x = 1.238726945 + -0.6333333335 Combine like terms: 1.238726945 + -0.6333333335 = 0.6053936115 x = 0.6053936115 Simplifying x = 0.6053936115Subproblem 2
x + 0.6333333335 = -1.238726945 Simplifying x + 0.6333333335 = -1.238726945 Reorder the terms: 0.6333333335 + x = -1.238726945 Solving 0.6333333335 + x = -1.238726945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6333333335' to each side of the equation. 0.6333333335 + -0.6333333335 + x = -1.238726945 + -0.6333333335 Combine like terms: 0.6333333335 + -0.6333333335 = 0.0000000000 0.0000000000 + x = -1.238726945 + -0.6333333335 x = -1.238726945 + -0.6333333335 Combine like terms: -1.238726945 + -0.6333333335 = -1.8720602785 x = -1.8720602785 Simplifying x = -1.8720602785Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6053936115, -1.8720602785}
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