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Simplifying 5x2 + 39x + -53 = 0 Reorder the terms: -53 + 39x + 5x2 = 0 Solving -53 + 39x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -10.6 + 7.8x + x2 = 0 Move the constant term to the right: Add '10.6' to each side of the equation. -10.6 + 7.8x + 10.6 + x2 = 0 + 10.6 Reorder the terms: -10.6 + 10.6 + 7.8x + x2 = 0 + 10.6 Combine like terms: -10.6 + 10.6 = 0.0 0.0 + 7.8x + x2 = 0 + 10.6 7.8x + x2 = 0 + 10.6 Combine like terms: 0 + 10.6 = 10.6 7.8x + x2 = 10.6 The x term is 7.8x. Take half its coefficient (3.9). Square it (15.21) and add it to both sides. Add '15.21' to each side of the equation. 7.8x + 15.21 + x2 = 10.6 + 15.21 Reorder the terms: 15.21 + 7.8x + x2 = 10.6 + 15.21 Combine like terms: 10.6 + 15.21 = 25.81 15.21 + 7.8x + x2 = 25.81 Factor a perfect square on the left side: (x + 3.9)(x + 3.9) = 25.81 Calculate the square root of the right side: 5.080354318 Break this problem into two subproblems by setting (x + 3.9) equal to 5.080354318 and -5.080354318.Subproblem 1
x + 3.9 = 5.080354318 Simplifying x + 3.9 = 5.080354318 Reorder the terms: 3.9 + x = 5.080354318 Solving 3.9 + x = 5.080354318 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.9' to each side of the equation. 3.9 + -3.9 + x = 5.080354318 + -3.9 Combine like terms: 3.9 + -3.9 = 0.0 0.0 + x = 5.080354318 + -3.9 x = 5.080354318 + -3.9 Combine like terms: 5.080354318 + -3.9 = 1.180354318 x = 1.180354318 Simplifying x = 1.180354318Subproblem 2
x + 3.9 = -5.080354318 Simplifying x + 3.9 = -5.080354318 Reorder the terms: 3.9 + x = -5.080354318 Solving 3.9 + x = -5.080354318 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.9' to each side of the equation. 3.9 + -3.9 + x = -5.080354318 + -3.9 Combine like terms: 3.9 + -3.9 = 0.0 0.0 + x = -5.080354318 + -3.9 x = -5.080354318 + -3.9 Combine like terms: -5.080354318 + -3.9 = -8.980354318 x = -8.980354318 Simplifying x = -8.980354318Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.180354318, -8.980354318}
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