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Simplifying 5x2 + 34x + 42 = 0 Reorder the terms: 42 + 34x + 5x2 = 0 Solving 42 + 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'. 8.4 + 6.8x + x2 = 0 Move the constant term to the right: Add '-8.4' to each side of the equation. 8.4 + 6.8x + -8.4 + x2 = 0 + -8.4 Reorder the terms: 8.4 + -8.4 + 6.8x + x2 = 0 + -8.4 Combine like terms: 8.4 + -8.4 = 0.0 0.0 + 6.8x + x2 = 0 + -8.4 6.8x + x2 = 0 + -8.4 Combine like terms: 0 + -8.4 = -8.4 6.8x + x2 = -8.4 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 = -8.4 + 11.56 Reorder the terms: 11.56 + 6.8x + x2 = -8.4 + 11.56 Combine like terms: -8.4 + 11.56 = 3.16 11.56 + 6.8x + x2 = 3.16 Factor a perfect square on the left side: (x + 3.4)(x + 3.4) = 3.16 Calculate the square root of the right side: 1.777638883 Break this problem into two subproblems by setting (x + 3.4) equal to 1.777638883 and -1.777638883.Subproblem 1
x + 3.4 = 1.777638883 Simplifying x + 3.4 = 1.777638883 Reorder the terms: 3.4 + x = 1.777638883 Solving 3.4 + x = 1.777638883 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 = 1.777638883 + -3.4 Combine like terms: 3.4 + -3.4 = 0.0 0.0 + x = 1.777638883 + -3.4 x = 1.777638883 + -3.4 Combine like terms: 1.777638883 + -3.4 = -1.622361117 x = -1.622361117 Simplifying x = -1.622361117Subproblem 2
x + 3.4 = -1.777638883 Simplifying x + 3.4 = -1.777638883 Reorder the terms: 3.4 + x = -1.777638883 Solving 3.4 + x = -1.777638883 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 = -1.777638883 + -3.4 Combine like terms: 3.4 + -3.4 = 0.0 0.0 + x = -1.777638883 + -3.4 x = -1.777638883 + -3.4 Combine like terms: -1.777638883 + -3.4 = -5.177638883 x = -5.177638883 Simplifying x = -5.177638883Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.622361117, -5.177638883}
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