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Simplifying 5x2 + 14x + -20 = 0 Reorder the terms: -20 + 14x + 5x2 = 0 Solving -20 + 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'. -4 + 2.8x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 2.8x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 2.8x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 2.8x + x2 = 0 + 4 2.8x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 2.8x + x2 = 4 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 = 4 + 1.96 Reorder the terms: 1.96 + 2.8x + x2 = 4 + 1.96 Combine like terms: 4 + 1.96 = 5.96 1.96 + 2.8x + x2 = 5.96 Factor a perfect square on the left side: (x + 1.4)(x + 1.4) = 5.96 Calculate the square root of the right side: 2.441311123 Break this problem into two subproblems by setting (x + 1.4) equal to 2.441311123 and -2.441311123.Subproblem 1
x + 1.4 = 2.441311123 Simplifying x + 1.4 = 2.441311123 Reorder the terms: 1.4 + x = 2.441311123 Solving 1.4 + x = 2.441311123 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 = 2.441311123 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + x = 2.441311123 + -1.4 x = 2.441311123 + -1.4 Combine like terms: 2.441311123 + -1.4 = 1.041311123 x = 1.041311123 Simplifying x = 1.041311123Subproblem 2
x + 1.4 = -2.441311123 Simplifying x + 1.4 = -2.441311123 Reorder the terms: 1.4 + x = -2.441311123 Solving 1.4 + x = -2.441311123 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 = -2.441311123 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + x = -2.441311123 + -1.4 x = -2.441311123 + -1.4 Combine like terms: -2.441311123 + -1.4 = -3.841311123 x = -3.841311123 Simplifying x = -3.841311123Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.041311123, -3.841311123}
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