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Simplifying 4x2 + 19x + 20 = 0 Reorder the terms: 20 + 19x + 4x2 = 0 Solving 20 + 19x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 5 + 4.75x + x2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + 4.75x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + 4.75x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4.75x + x2 = 0 + -5 4.75x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 4.75x + x2 = -5 The x term is 4.75x. Take half its coefficient (2.375). Square it (5.640625) and add it to both sides. Add '5.640625' to each side of the equation. 4.75x + 5.640625 + x2 = -5 + 5.640625 Reorder the terms: 5.640625 + 4.75x + x2 = -5 + 5.640625 Combine like terms: -5 + 5.640625 = 0.640625 5.640625 + 4.75x + x2 = 0.640625 Factor a perfect square on the left side: (x + 2.375)(x + 2.375) = 0.640625 Calculate the square root of the right side: 0.80039053 Break this problem into two subproblems by setting (x + 2.375) equal to 0.80039053 and -0.80039053.Subproblem 1
x + 2.375 = 0.80039053 Simplifying x + 2.375 = 0.80039053 Reorder the terms: 2.375 + x = 0.80039053 Solving 2.375 + x = 0.80039053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.375' to each side of the equation. 2.375 + -2.375 + x = 0.80039053 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + x = 0.80039053 + -2.375 x = 0.80039053 + -2.375 Combine like terms: 0.80039053 + -2.375 = -1.57460947 x = -1.57460947 Simplifying x = -1.57460947Subproblem 2
x + 2.375 = -0.80039053 Simplifying x + 2.375 = -0.80039053 Reorder the terms: 2.375 + x = -0.80039053 Solving 2.375 + x = -0.80039053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.375' to each side of the equation. 2.375 + -2.375 + x = -0.80039053 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + x = -0.80039053 + -2.375 x = -0.80039053 + -2.375 Combine like terms: -0.80039053 + -2.375 = -3.17539053 x = -3.17539053 Simplifying x = -3.17539053Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.57460947, -3.17539053}
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