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Simplifying (8x + 5)(3x + 1) + -12 = 4 Reorder the terms: (5 + 8x)(3x + 1) + -12 = 4 Reorder the terms: (5 + 8x)(1 + 3x) + -12 = 4 Multiply (5 + 8x) * (1 + 3x) (5(1 + 3x) + 8x * (1 + 3x)) + -12 = 4 ((1 * 5 + 3x * 5) + 8x * (1 + 3x)) + -12 = 4 ((5 + 15x) + 8x * (1 + 3x)) + -12 = 4 (5 + 15x + (1 * 8x + 3x * 8x)) + -12 = 4 (5 + 15x + (8x + 24x2)) + -12 = 4 Combine like terms: 15x + 8x = 23x (5 + 23x + 24x2) + -12 = 4 Reorder the terms: 5 + -12 + 23x + 24x2 = 4 Combine like terms: 5 + -12 = -7 -7 + 23x + 24x2 = 4 Solving -7 + 23x + 24x2 = 4 Solving for variable 'x'. Reorder the terms: -7 + -4 + 23x + 24x2 = 4 + -4 Combine like terms: -7 + -4 = -11 -11 + 23x + 24x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -11 + 23x + 24x2 = 0 Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -0.4583333333 + 0.9583333333x + x2 = 0 Move the constant term to the right: Add '0.4583333333' to each side of the equation. -0.4583333333 + 0.9583333333x + 0.4583333333 + x2 = 0 + 0.4583333333 Reorder the terms: -0.4583333333 + 0.4583333333 + 0.9583333333x + x2 = 0 + 0.4583333333 Combine like terms: -0.4583333333 + 0.4583333333 = 0.0000000000 0.0000000000 + 0.9583333333x + x2 = 0 + 0.4583333333 0.9583333333x + x2 = 0 + 0.4583333333 Combine like terms: 0 + 0.4583333333 = 0.4583333333 0.9583333333x + x2 = 0.4583333333 The x term is 0.9583333333x. Take half its coefficient (0.4791666667). Square it (0.2296006945) and add it to both sides. Add '0.2296006945' to each side of the equation. 0.9583333333x + 0.2296006945 + x2 = 0.4583333333 + 0.2296006945 Reorder the terms: 0.2296006945 + 0.9583333333x + x2 = 0.4583333333 + 0.2296006945 Combine like terms: 0.4583333333 + 0.2296006945 = 0.6879340278 0.2296006945 + 0.9583333333x + x2 = 0.6879340278 Factor a perfect square on the left side: (x + 0.4791666667)(x + 0.4791666667) = 0.6879340278 Calculate the square root of the right side: 0.829417885 Break this problem into two subproblems by setting (x + 0.4791666667) equal to 0.829417885 and -0.829417885.Subproblem 1
x + 0.4791666667 = 0.829417885 Simplifying x + 0.4791666667 = 0.829417885 Reorder the terms: 0.4791666667 + x = 0.829417885 Solving 0.4791666667 + x = 0.829417885 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4791666667' to each side of the equation. 0.4791666667 + -0.4791666667 + x = 0.829417885 + -0.4791666667 Combine like terms: 0.4791666667 + -0.4791666667 = 0.0000000000 0.0000000000 + x = 0.829417885 + -0.4791666667 x = 0.829417885 + -0.4791666667 Combine like terms: 0.829417885 + -0.4791666667 = 0.3502512183 x = 0.3502512183 Simplifying x = 0.3502512183Subproblem 2
x + 0.4791666667 = -0.829417885 Simplifying x + 0.4791666667 = -0.829417885 Reorder the terms: 0.4791666667 + x = -0.829417885 Solving 0.4791666667 + x = -0.829417885 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4791666667' to each side of the equation. 0.4791666667 + -0.4791666667 + x = -0.829417885 + -0.4791666667 Combine like terms: 0.4791666667 + -0.4791666667 = 0.0000000000 0.0000000000 + x = -0.829417885 + -0.4791666667 x = -0.829417885 + -0.4791666667 Combine like terms: -0.829417885 + -0.4791666667 = -1.3085845517 x = -1.3085845517 Simplifying x = -1.3085845517Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3502512183, -1.3085845517}
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