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Simplifying 5x2 + 26x + 22 = 0 Reorder the terms: 22 + 26x + 5x2 = 0 Solving 22 + 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'. 4.4 + 5.2x + x2 = 0 Move the constant term to the right: Add '-4.4' to each side of the equation. 4.4 + 5.2x + -4.4 + x2 = 0 + -4.4 Reorder the terms: 4.4 + -4.4 + 5.2x + x2 = 0 + -4.4 Combine like terms: 4.4 + -4.4 = 0.0 0.0 + 5.2x + x2 = 0 + -4.4 5.2x + x2 = 0 + -4.4 Combine like terms: 0 + -4.4 = -4.4 5.2x + x2 = -4.4 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 = -4.4 + 6.76 Reorder the terms: 6.76 + 5.2x + x2 = -4.4 + 6.76 Combine like terms: -4.4 + 6.76 = 2.36 6.76 + 5.2x + x2 = 2.36 Factor a perfect square on the left side: (x + 2.6)(x + 2.6) = 2.36 Calculate the square root of the right side: 1.53622915 Break this problem into two subproblems by setting (x + 2.6) equal to 1.53622915 and -1.53622915.Subproblem 1
x + 2.6 = 1.53622915 Simplifying x + 2.6 = 1.53622915 Reorder the terms: 2.6 + x = 1.53622915 Solving 2.6 + x = 1.53622915 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 = 1.53622915 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + x = 1.53622915 + -2.6 x = 1.53622915 + -2.6 Combine like terms: 1.53622915 + -2.6 = -1.06377085 x = -1.06377085 Simplifying x = -1.06377085Subproblem 2
x + 2.6 = -1.53622915 Simplifying x + 2.6 = -1.53622915 Reorder the terms: 2.6 + x = -1.53622915 Solving 2.6 + x = -1.53622915 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 = -1.53622915 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + x = -1.53622915 + -2.6 x = -1.53622915 + -2.6 Combine like terms: -1.53622915 + -2.6 = -4.13622915 x = -4.13622915 Simplifying x = -4.13622915Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.06377085, -4.13622915}
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