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Simplifying 5x2 + 14x + 5 = 0 Reorder the terms: 5 + 14x + 5x2 = 0 Solving 5 + 14x + 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 + 2.8x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 2.8x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 2.8x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2.8x + x2 = 0 + -1 2.8x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 2.8x + x2 = -1 The x term is 2.8x. Take half its coefficient (1.4). Square it (1.96) and add it to both sides. Add '1.96' to each side of the equation. 2.8x + 1.96 + x2 = -1 + 1.96 Reorder the terms: 1.96 + 2.8x + x2 = -1 + 1.96 Combine like terms: -1 + 1.96 = 0.96 1.96 + 2.8x + x2 = 0.96 Factor a perfect square on the left side: (x + 1.4)(x + 1.4) = 0.96 Calculate the square root of the right side: 0.979795897 Break this problem into two subproblems by setting (x + 1.4) equal to 0.979795897 and -0.979795897.Subproblem 1
x + 1.4 = 0.979795897 Simplifying x + 1.4 = 0.979795897 Reorder the terms: 1.4 + x = 0.979795897 Solving 1.4 + x = 0.979795897 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.4' to each side of the equation. 1.4 + -1.4 + x = 0.979795897 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + x = 0.979795897 + -1.4 x = 0.979795897 + -1.4 Combine like terms: 0.979795897 + -1.4 = -0.420204103 x = -0.420204103 Simplifying x = -0.420204103Subproblem 2
x + 1.4 = -0.979795897 Simplifying x + 1.4 = -0.979795897 Reorder the terms: 1.4 + x = -0.979795897 Solving 1.4 + x = -0.979795897 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.4' to each side of the equation. 1.4 + -1.4 + x = -0.979795897 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + x = -0.979795897 + -1.4 x = -0.979795897 + -1.4 Combine like terms: -0.979795897 + -1.4 = -2.379795897 x = -2.379795897 Simplifying x = -2.379795897Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.420204103, -2.379795897}
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