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Simplifying 5x2 + 26x + 6 = 0 Reorder the terms: 6 + 26x + 5x2 = 0 Solving 6 + 26x + 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'. 1.2 + 5.2x + x2 = 0 Move the constant term to the right: Add '-1.2' to each side of the equation. 1.2 + 5.2x + -1.2 + x2 = 0 + -1.2 Reorder the terms: 1.2 + -1.2 + 5.2x + x2 = 0 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + 5.2x + x2 = 0 + -1.2 5.2x + x2 = 0 + -1.2 Combine like terms: 0 + -1.2 = -1.2 5.2x + x2 = -1.2 The x term is 5.2x. Take half its coefficient (2.6). Square it (6.76) and add it to both sides. Add '6.76' to each side of the equation. 5.2x + 6.76 + x2 = -1.2 + 6.76 Reorder the terms: 6.76 + 5.2x + x2 = -1.2 + 6.76 Combine like terms: -1.2 + 6.76 = 5.56 6.76 + 5.2x + x2 = 5.56 Factor a perfect square on the left side: (x + 2.6)(x + 2.6) = 5.56 Calculate the square root of the right side: 2.357965225 Break this problem into two subproblems by setting (x + 2.6) equal to 2.357965225 and -2.357965225.Subproblem 1
x + 2.6 = 2.357965225 Simplifying x + 2.6 = 2.357965225 Reorder the terms: 2.6 + x = 2.357965225 Solving 2.6 + x = 2.357965225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.6' to each side of the equation. 2.6 + -2.6 + x = 2.357965225 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + x = 2.357965225 + -2.6 x = 2.357965225 + -2.6 Combine like terms: 2.357965225 + -2.6 = -0.242034775 x = -0.242034775 Simplifying x = -0.242034775Subproblem 2
x + 2.6 = -2.357965225 Simplifying x + 2.6 = -2.357965225 Reorder the terms: 2.6 + x = -2.357965225 Solving 2.6 + x = -2.357965225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.6' to each side of the equation. 2.6 + -2.6 + x = -2.357965225 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + x = -2.357965225 + -2.6 x = -2.357965225 + -2.6 Combine like terms: -2.357965225 + -2.6 = -4.957965225 x = -4.957965225 Simplifying x = -4.957965225Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.242034775, -4.957965225}
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