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Simplifying (14x + 5)(14x + 5) = 20 Reorder the terms: (5 + 14x)(14x + 5) = 20 Reorder the terms: (5 + 14x)(5 + 14x) = 20 Multiply (5 + 14x) * (5 + 14x) (5(5 + 14x) + 14x * (5 + 14x)) = 20 ((5 * 5 + 14x * 5) + 14x * (5 + 14x)) = 20 ((25 + 70x) + 14x * (5 + 14x)) = 20 (25 + 70x + (5 * 14x + 14x * 14x)) = 20 (25 + 70x + (70x + 196x2)) = 20 Combine like terms: 70x + 70x = 140x (25 + 140x + 196x2) = 20 Solving 25 + 140x + 196x2 = 20 Solving for variable 'x'. Reorder the terms: 25 + -20 + 140x + 196x2 = 20 + -20 Combine like terms: 25 + -20 = 5 5 + 140x + 196x2 = 20 + -20 Combine like terms: 20 + -20 = 0 5 + 140x + 196x2 = 0 Begin completing the square. Divide all terms by 196 the coefficient of the squared term: Divide each side by '196'. 0.02551020408 + 0.7142857143x + x2 = 0 Move the constant term to the right: Add '-0.02551020408' to each side of the equation. 0.02551020408 + 0.7142857143x + -0.02551020408 + x2 = 0 + -0.02551020408 Reorder the terms: 0.02551020408 + -0.02551020408 + 0.7142857143x + x2 = 0 + -0.02551020408 Combine like terms: 0.02551020408 + -0.02551020408 = 0.00000000000 0.00000000000 + 0.7142857143x + x2 = 0 + -0.02551020408 0.7142857143x + x2 = 0 + -0.02551020408 Combine like terms: 0 + -0.02551020408 = -0.02551020408 0.7142857143x + x2 = -0.02551020408 The x term is 0.7142857143x. Take half its coefficient (0.3571428572). Square it (0.1275510204) and add it to both sides. Add '0.1275510204' to each side of the equation. 0.7142857143x + 0.1275510204 + x2 = -0.02551020408 + 0.1275510204 Reorder the terms: 0.1275510204 + 0.7142857143x + x2 = -0.02551020408 + 0.1275510204 Combine like terms: -0.02551020408 + 0.1275510204 = 0.10204081632 0.1275510204 + 0.7142857143x + x2 = 0.10204081632 Factor a perfect square on the left side: (x + 0.3571428572)(x + 0.3571428572) = 0.10204081632 Calculate the square root of the right side: 0.319438282 Break this problem into two subproblems by setting (x + 0.3571428572) equal to 0.319438282 and -0.319438282.Subproblem 1
x + 0.3571428572 = 0.319438282 Simplifying x + 0.3571428572 = 0.319438282 Reorder the terms: 0.3571428572 + x = 0.319438282 Solving 0.3571428572 + x = 0.319438282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3571428572' to each side of the equation. 0.3571428572 + -0.3571428572 + x = 0.319438282 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + x = 0.319438282 + -0.3571428572 x = 0.319438282 + -0.3571428572 Combine like terms: 0.319438282 + -0.3571428572 = -0.0377045752 x = -0.0377045752 Simplifying x = -0.0377045752Subproblem 2
x + 0.3571428572 = -0.319438282 Simplifying x + 0.3571428572 = -0.319438282 Reorder the terms: 0.3571428572 + x = -0.319438282 Solving 0.3571428572 + x = -0.319438282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3571428572' to each side of the equation. 0.3571428572 + -0.3571428572 + x = -0.319438282 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + x = -0.319438282 + -0.3571428572 x = -0.319438282 + -0.3571428572 Combine like terms: -0.319438282 + -0.3571428572 = -0.6765811392 x = -0.6765811392 Simplifying x = -0.6765811392Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.0377045752, -0.6765811392}
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