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Simplifying 5x2 + 34x + -22 = 0 Reorder the terms: -22 + 34x + 5x2 = 0 Solving -22 + 34x + 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 + 6.8x + x2 = 0 Move the constant term to the right: Add '4.4' to each side of the equation. -4.4 + 6.8x + 4.4 + x2 = 0 + 4.4 Reorder the terms: -4.4 + 4.4 + 6.8x + x2 = 0 + 4.4 Combine like terms: -4.4 + 4.4 = 0.0 0.0 + 6.8x + x2 = 0 + 4.4 6.8x + x2 = 0 + 4.4 Combine like terms: 0 + 4.4 = 4.4 6.8x + x2 = 4.4 The x term is 6.8x. Take half its coefficient (3.4). Square it (11.56) and add it to both sides. Add '11.56' to each side of the equation. 6.8x + 11.56 + x2 = 4.4 + 11.56 Reorder the terms: 11.56 + 6.8x + x2 = 4.4 + 11.56 Combine like terms: 4.4 + 11.56 = 15.96 11.56 + 6.8x + x2 = 15.96 Factor a perfect square on the left side: (x + 3.4)(x + 3.4) = 15.96 Calculate the square root of the right side: 3.994996871 Break this problem into two subproblems by setting (x + 3.4) equal to 3.994996871 and -3.994996871.Subproblem 1
x + 3.4 = 3.994996871 Simplifying x + 3.4 = 3.994996871 Reorder the terms: 3.4 + x = 3.994996871 Solving 3.4 + x = 3.994996871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.4' to each side of the equation. 3.4 + -3.4 + x = 3.994996871 + -3.4 Combine like terms: 3.4 + -3.4 = 0.0 0.0 + x = 3.994996871 + -3.4 x = 3.994996871 + -3.4 Combine like terms: 3.994996871 + -3.4 = 0.594996871 x = 0.594996871 Simplifying x = 0.594996871Subproblem 2
x + 3.4 = -3.994996871 Simplifying x + 3.4 = -3.994996871 Reorder the terms: 3.4 + x = -3.994996871 Solving 3.4 + x = -3.994996871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.4' to each side of the equation. 3.4 + -3.4 + x = -3.994996871 + -3.4 Combine like terms: 3.4 + -3.4 = 0.0 0.0 + x = -3.994996871 + -3.4 x = -3.994996871 + -3.4 Combine like terms: -3.994996871 + -3.4 = -7.394996871 x = -7.394996871 Simplifying x = -7.394996871Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.594996871, -7.394996871}
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