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Simplifying 7(4 + 2x)(28 + 14x) = 3 Multiply (4 + 2x) * (28 + 14x) 7(4(28 + 14x) + 2x * (28 + 14x)) = 3 7((28 * 4 + 14x * 4) + 2x * (28 + 14x)) = 3 7((112 + 56x) + 2x * (28 + 14x)) = 3 7(112 + 56x + (28 * 2x + 14x * 2x)) = 3 7(112 + 56x + (56x + 28x2)) = 3 Combine like terms: 56x + 56x = 112x 7(112 + 112x + 28x2) = 3 (112 * 7 + 112x * 7 + 28x2 * 7) = 3 (784 + 784x + 196x2) = 3 Solving 784 + 784x + 196x2 = 3 Solving for variable 'x'. Reorder the terms: 784 + -3 + 784x + 196x2 = 3 + -3 Combine like terms: 784 + -3 = 781 781 + 784x + 196x2 = 3 + -3 Combine like terms: 3 + -3 = 0 781 + 784x + 196x2 = 0 Begin completing the square. Divide all terms by 196 the coefficient of the squared term: Divide each side by '196'. 3.984693878 + 4x + x2 = 0 Move the constant term to the right: Add '-3.984693878' to each side of the equation. 3.984693878 + 4x + -3.984693878 + x2 = 0 + -3.984693878 Reorder the terms: 3.984693878 + -3.984693878 + 4x + x2 = 0 + -3.984693878 Combine like terms: 3.984693878 + -3.984693878 = 0.000000000 0.000000000 + 4x + x2 = 0 + -3.984693878 4x + x2 = 0 + -3.984693878 Combine like terms: 0 + -3.984693878 = -3.984693878 4x + x2 = -3.984693878 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = -3.984693878 + 4 Reorder the terms: 4 + 4x + x2 = -3.984693878 + 4 Combine like terms: -3.984693878 + 4 = 0.015306122 4 + 4x + x2 = 0.015306122 Factor a perfect square on the left side: (x + 2)(x + 2) = 0.015306122 Calculate the square root of the right side: 0.123717913 Break this problem into two subproblems by setting (x + 2) equal to 0.123717913 and -0.123717913.Subproblem 1
x + 2 = 0.123717913 Simplifying x + 2 = 0.123717913 Reorder the terms: 2 + x = 0.123717913 Solving 2 + x = 0.123717913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0.123717913 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0.123717913 + -2 x = 0.123717913 + -2 Combine like terms: 0.123717913 + -2 = -1.876282087 x = -1.876282087 Simplifying x = -1.876282087Subproblem 2
x + 2 = -0.123717913 Simplifying x + 2 = -0.123717913 Reorder the terms: 2 + x = -0.123717913 Solving 2 + x = -0.123717913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -0.123717913 + -2 Combine like terms: 2 + -2 = 0 0 + x = -0.123717913 + -2 x = -0.123717913 + -2 Combine like terms: -0.123717913 + -2 = -2.123717913 x = -2.123717913 Simplifying x = -2.123717913Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.876282087, -2.123717913}
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