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Simplifying 5x2 + 34x + 25 = 0 Reorder the terms: 25 + 34x + 5x2 = 0 Solving 25 + 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'. 5 + 6.8x + x2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + 6.8x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + 6.8x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 6.8x + x2 = 0 + -5 6.8x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 6.8x + x2 = -5 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 = -5 + 11.56 Reorder the terms: 11.56 + 6.8x + x2 = -5 + 11.56 Combine like terms: -5 + 11.56 = 6.56 11.56 + 6.8x + x2 = 6.56 Factor a perfect square on the left side: (x + 3.4)(x + 3.4) = 6.56 Calculate the square root of the right side: 2.561249695 Break this problem into two subproblems by setting (x + 3.4) equal to 2.561249695 and -2.561249695.Subproblem 1
x + 3.4 = 2.561249695 Simplifying x + 3.4 = 2.561249695 Reorder the terms: 3.4 + x = 2.561249695 Solving 3.4 + x = 2.561249695 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 = 2.561249695 + -3.4 Combine like terms: 3.4 + -3.4 = 0.0 0.0 + x = 2.561249695 + -3.4 x = 2.561249695 + -3.4 Combine like terms: 2.561249695 + -3.4 = -0.838750305 x = -0.838750305 Simplifying x = -0.838750305Subproblem 2
x + 3.4 = -2.561249695 Simplifying x + 3.4 = -2.561249695 Reorder the terms: 3.4 + x = -2.561249695 Solving 3.4 + x = -2.561249695 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 = -2.561249695 + -3.4 Combine like terms: 3.4 + -3.4 = 0.0 0.0 + x = -2.561249695 + -3.4 x = -2.561249695 + -3.4 Combine like terms: -2.561249695 + -3.4 = -5.961249695 x = -5.961249695 Simplifying x = -5.961249695Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.838750305, -5.961249695}
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