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Simplifying 5x2 + 14x + -25 = 0 Reorder the terms: -25 + 14x + 5x2 = 0 Solving -25 + 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'. -5 + 2.8x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 2.8x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 2.8x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 2.8x + x2 = 0 + 5 2.8x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 2.8x + x2 = 5 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 = 5 + 1.96 Reorder the terms: 1.96 + 2.8x + x2 = 5 + 1.96 Combine like terms: 5 + 1.96 = 6.96 1.96 + 2.8x + x2 = 6.96 Factor a perfect square on the left side: (x + 1.4)(x + 1.4) = 6.96 Calculate the square root of the right side: 2.638181192 Break this problem into two subproblems by setting (x + 1.4) equal to 2.638181192 and -2.638181192.Subproblem 1
x + 1.4 = 2.638181192 Simplifying x + 1.4 = 2.638181192 Reorder the terms: 1.4 + x = 2.638181192 Solving 1.4 + x = 2.638181192 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 = 2.638181192 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + x = 2.638181192 + -1.4 x = 2.638181192 + -1.4 Combine like terms: 2.638181192 + -1.4 = 1.238181192 x = 1.238181192 Simplifying x = 1.238181192Subproblem 2
x + 1.4 = -2.638181192 Simplifying x + 1.4 = -2.638181192 Reorder the terms: 1.4 + x = -2.638181192 Solving 1.4 + x = -2.638181192 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 = -2.638181192 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + x = -2.638181192 + -1.4 x = -2.638181192 + -1.4 Combine like terms: -2.638181192 + -1.4 = -4.038181192 x = -4.038181192 Simplifying x = -4.038181192Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.238181192, -4.038181192}
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