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Simplifying 20x2 + 52x + 19 = 0 Reorder the terms: 19 + 52x + 20x2 = 0 Solving 19 + 52x + 20x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. 0.95 + 2.6x + x2 = 0 Move the constant term to the right: Add '-0.95' to each side of the equation. 0.95 + 2.6x + -0.95 + x2 = 0 + -0.95 Reorder the terms: 0.95 + -0.95 + 2.6x + x2 = 0 + -0.95 Combine like terms: 0.95 + -0.95 = 0.00 0.00 + 2.6x + x2 = 0 + -0.95 2.6x + x2 = 0 + -0.95 Combine like terms: 0 + -0.95 = -0.95 2.6x + x2 = -0.95 The x term is 2.6x. Take half its coefficient (1.3). Square it (1.69) and add it to both sides. Add '1.69' to each side of the equation. 2.6x + 1.69 + x2 = -0.95 + 1.69 Reorder the terms: 1.69 + 2.6x + x2 = -0.95 + 1.69 Combine like terms: -0.95 + 1.69 = 0.74 1.69 + 2.6x + x2 = 0.74 Factor a perfect square on the left side: (x + 1.3)(x + 1.3) = 0.74 Calculate the square root of the right side: 0.860232527 Break this problem into two subproblems by setting (x + 1.3) equal to 0.860232527 and -0.860232527.Subproblem 1
x + 1.3 = 0.860232527 Simplifying x + 1.3 = 0.860232527 Reorder the terms: 1.3 + x = 0.860232527 Solving 1.3 + x = 0.860232527 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.3' to each side of the equation. 1.3 + -1.3 + x = 0.860232527 + -1.3 Combine like terms: 1.3 + -1.3 = 0.0 0.0 + x = 0.860232527 + -1.3 x = 0.860232527 + -1.3 Combine like terms: 0.860232527 + -1.3 = -0.439767473 x = -0.439767473 Simplifying x = -0.439767473Subproblem 2
x + 1.3 = -0.860232527 Simplifying x + 1.3 = -0.860232527 Reorder the terms: 1.3 + x = -0.860232527 Solving 1.3 + x = -0.860232527 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.3' to each side of the equation. 1.3 + -1.3 + x = -0.860232527 + -1.3 Combine like terms: 1.3 + -1.3 = 0.0 0.0 + x = -0.860232527 + -1.3 x = -0.860232527 + -1.3 Combine like terms: -0.860232527 + -1.3 = -2.160232527 x = -2.160232527 Simplifying x = -2.160232527Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.439767473, -2.160232527}
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