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Simplifying 5x2 + -19x = 14 Reorder the terms: -19x + 5x2 = 14 Solving -19x + 5x2 = 14 Solving for variable 'x'. Reorder the terms: -14 + -19x + 5x2 = 14 + -14 Combine like terms: 14 + -14 = 0 -14 + -19x + 5x2 = 0 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 = 4.43179778 x = 4.43179778 Simplifying x = 4.43179778Subproblem 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 = -0.63179778 x = -0.63179778 Simplifying x = -0.63179778Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.43179778, -0.63179778}
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