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Simplifying 0 = 5x2 + 19x + -54 Reorder the terms: 0 = -54 + 19x + 5x2 Solving 0 = -54 + 19x + 5x2 Solving for variable 'x'. Combine like terms: 0 + 54 = 54 54 + -19x + -5x2 = -54 + 19x + 5x2 + 54 + -19x + -5x2 Reorder the terms: 54 + -19x + -5x2 = -54 + 54 + 19x + -19x + 5x2 + -5x2 Combine like terms: -54 + 54 = 0 54 + -19x + -5x2 = 0 + 19x + -19x + 5x2 + -5x2 54 + -19x + -5x2 = 19x + -19x + 5x2 + -5x2 Combine like terms: 19x + -19x = 0 54 + -19x + -5x2 = 0 + 5x2 + -5x2 54 + -19x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 54 + -19x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -10.8 + 3.8x + x2 = 0 Move the constant term to the right: Add '10.8' to each side of the equation. -10.8 + 3.8x + 10.8 + x2 = 0 + 10.8 Reorder the terms: -10.8 + 10.8 + 3.8x + x2 = 0 + 10.8 Combine like terms: -10.8 + 10.8 = 0.0 0.0 + 3.8x + x2 = 0 + 10.8 3.8x + x2 = 0 + 10.8 Combine like terms: 0 + 10.8 = 10.8 3.8x + x2 = 10.8 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 = 10.8 + 3.61 Reorder the terms: 3.61 + 3.8x + x2 = 10.8 + 3.61 Combine like terms: 10.8 + 3.61 = 14.41 3.61 + 3.8x + x2 = 14.41 Factor a perfect square on the left side: (x + 1.9)(x + 1.9) = 14.41 Calculate the square root of the right side: 3.796050579 Break this problem into two subproblems by setting (x + 1.9) equal to 3.796050579 and -3.796050579.Subproblem 1
x + 1.9 = 3.796050579 Simplifying x + 1.9 = 3.796050579 Reorder the terms: 1.9 + x = 3.796050579 Solving 1.9 + x = 3.796050579 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 = 3.796050579 + -1.9 Combine like terms: 1.9 + -1.9 = 0.0 0.0 + x = 3.796050579 + -1.9 x = 3.796050579 + -1.9 Combine like terms: 3.796050579 + -1.9 = 1.896050579 x = 1.896050579 Simplifying x = 1.896050579Subproblem 2
x + 1.9 = -3.796050579 Simplifying x + 1.9 = -3.796050579 Reorder the terms: 1.9 + x = -3.796050579 Solving 1.9 + x = -3.796050579 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 = -3.796050579 + -1.9 Combine like terms: 1.9 + -1.9 = 0.0 0.0 + x = -3.796050579 + -1.9 x = -3.796050579 + -1.9 Combine like terms: -3.796050579 + -1.9 = -5.696050579 x = -5.696050579 Simplifying x = -5.696050579Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.896050579, -5.696050579}
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