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Simplifying 5x2 + 17x + 13 = 0 Reorder the terms: 13 + 17x + 5x2 = 0 Solving 13 + 17x + 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'. 2.6 + 3.4x + x2 = 0 Move the constant term to the right: Add '-2.6' to each side of the equation. 2.6 + 3.4x + -2.6 + x2 = 0 + -2.6 Reorder the terms: 2.6 + -2.6 + 3.4x + x2 = 0 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + 3.4x + x2 = 0 + -2.6 3.4x + x2 = 0 + -2.6 Combine like terms: 0 + -2.6 = -2.6 3.4x + x2 = -2.6 The x term is 3.4x. Take half its coefficient (1.7). Square it (2.89) and add it to both sides. Add '2.89' to each side of the equation. 3.4x + 2.89 + x2 = -2.6 + 2.89 Reorder the terms: 2.89 + 3.4x + x2 = -2.6 + 2.89 Combine like terms: -2.6 + 2.89 = 0.29 2.89 + 3.4x + x2 = 0.29 Factor a perfect square on the left side: (x + 1.7)(x + 1.7) = 0.29 Calculate the square root of the right side: 0.538516481 Break this problem into two subproblems by setting (x + 1.7) equal to 0.538516481 and -0.538516481.Subproblem 1
x + 1.7 = 0.538516481 Simplifying x + 1.7 = 0.538516481 Reorder the terms: 1.7 + x = 0.538516481 Solving 1.7 + x = 0.538516481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.7' to each side of the equation. 1.7 + -1.7 + x = 0.538516481 + -1.7 Combine like terms: 1.7 + -1.7 = 0.0 0.0 + x = 0.538516481 + -1.7 x = 0.538516481 + -1.7 Combine like terms: 0.538516481 + -1.7 = -1.161483519 x = -1.161483519 Simplifying x = -1.161483519Subproblem 2
x + 1.7 = -0.538516481 Simplifying x + 1.7 = -0.538516481 Reorder the terms: 1.7 + x = -0.538516481 Solving 1.7 + x = -0.538516481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.7' to each side of the equation. 1.7 + -1.7 + x = -0.538516481 + -1.7 Combine like terms: 1.7 + -1.7 = 0.0 0.0 + x = -0.538516481 + -1.7 x = -0.538516481 + -1.7 Combine like terms: -0.538516481 + -1.7 = -2.238516481 x = -2.238516481 Simplifying x = -2.238516481Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.161483519, -2.238516481}
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