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Simplifying 5x2 + 4x + -416 = 0 Reorder the terms: -416 + 4x + 5x2 = 0 Solving -416 + 4x + 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'. -83.2 + 0.8x + x2 = 0 Move the constant term to the right: Add '83.2' to each side of the equation. -83.2 + 0.8x + 83.2 + x2 = 0 + 83.2 Reorder the terms: -83.2 + 83.2 + 0.8x + x2 = 0 + 83.2 Combine like terms: -83.2 + 83.2 = 0.0 0.0 + 0.8x + x2 = 0 + 83.2 0.8x + x2 = 0 + 83.2 Combine like terms: 0 + 83.2 = 83.2 0.8x + x2 = 83.2 The x term is 0.8x. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8x + 0.16 + x2 = 83.2 + 0.16 Reorder the terms: 0.16 + 0.8x + x2 = 83.2 + 0.16 Combine like terms: 83.2 + 0.16 = 83.36 0.16 + 0.8x + x2 = 83.36 Factor a perfect square on the left side: (x + 0.4)(x + 0.4) = 83.36 Calculate the square root of the right side: 9.130169768 Break this problem into two subproblems by setting (x + 0.4) equal to 9.130169768 and -9.130169768.Subproblem 1
x + 0.4 = 9.130169768 Simplifying x + 0.4 = 9.130169768 Reorder the terms: 0.4 + x = 9.130169768 Solving 0.4 + x = 9.130169768 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = 9.130169768 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = 9.130169768 + -0.4 x = 9.130169768 + -0.4 Combine like terms: 9.130169768 + -0.4 = 8.730169768 x = 8.730169768 Simplifying x = 8.730169768Subproblem 2
x + 0.4 = -9.130169768 Simplifying x + 0.4 = -9.130169768 Reorder the terms: 0.4 + x = -9.130169768 Solving 0.4 + x = -9.130169768 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = -9.130169768 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = -9.130169768 + -0.4 x = -9.130169768 + -0.4 Combine like terms: -9.130169768 + -0.4 = -9.530169768 x = -9.530169768 Simplifying x = -9.530169768Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.730169768, -9.530169768}
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