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Simplifying 5x2 + 19x + -14 = 0 Reorder the terms: -14 + 19x + 5x2 = 0 Solving -14 + 19x + 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'. -2.8 + 3.8x + x2 = 0 Move the constant term to the right: Add '2.8' to each side of the equation. -2.8 + 3.8x + 2.8 + x2 = 0 + 2.8 Reorder the terms: -2.8 + 2.8 + 3.8x + x2 = 0 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + 3.8x + x2 = 0 + 2.8 3.8x + x2 = 0 + 2.8 Combine like terms: 0 + 2.8 = 2.8 3.8x + x2 = 2.8 The x term is 3.8x. Take half its coefficient (1.9). Square it (3.61) and add it to both sides. Add '3.61' to each side of the equation. 3.8x + 3.61 + x2 = 2.8 + 3.61 Reorder the terms: 3.61 + 3.8x + x2 = 2.8 + 3.61 Combine like terms: 2.8 + 3.61 = 6.41 3.61 + 3.8x + x2 = 6.41 Factor a perfect square on the left side: (x + 1.9)(x + 1.9) = 6.41 Calculate the square root of the right side: 2.53179778 Break this problem into two subproblems by setting (x + 1.9) equal to 2.53179778 and -2.53179778.Subproblem 1
x + 1.9 = 2.53179778 Simplifying x + 1.9 = 2.53179778 Reorder the terms: 1.9 + x = 2.53179778 Solving 1.9 + x = 2.53179778 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.9' to each side of the equation. 1.9 + -1.9 + x = 2.53179778 + -1.9 Combine like terms: 1.9 + -1.9 = 0.0 0.0 + x = 2.53179778 + -1.9 x = 2.53179778 + -1.9 Combine like terms: 2.53179778 + -1.9 = 0.63179778 x = 0.63179778 Simplifying x = 0.63179778Subproblem 2
x + 1.9 = -2.53179778 Simplifying x + 1.9 = -2.53179778 Reorder the terms: 1.9 + x = -2.53179778 Solving 1.9 + x = -2.53179778 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.9' to each side of the equation. 1.9 + -1.9 + x = -2.53179778 + -1.9 Combine like terms: 1.9 + -1.9 = 0.0 0.0 + x = -2.53179778 + -1.9 x = -2.53179778 + -1.9 Combine like terms: -2.53179778 + -1.9 = -4.43179778 x = -4.43179778 Simplifying x = -4.43179778Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.63179778, -4.43179778}
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