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Simplifying x2 + 3.8x + -17.1 = 0 Reorder the terms: -17.1 + 3.8x + x2 = 0 Solving -17.1 + 3.8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '17.1' to each side of the equation. -17.1 + 3.8x + 17.1 + x2 = 0 + 17.1 Reorder the terms: -17.1 + 17.1 + 3.8x + x2 = 0 + 17.1 Combine like terms: -17.1 + 17.1 = 0.0 0.0 + 3.8x + x2 = 0 + 17.1 3.8x + x2 = 0 + 17.1 Combine like terms: 0 + 17.1 = 17.1 3.8x + x2 = 17.1 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 = 17.1 + 3.61 Reorder the terms: 3.61 + 3.8x + x2 = 17.1 + 3.61 Combine like terms: 17.1 + 3.61 = 20.71 3.61 + 3.8x + x2 = 20.71 Factor a perfect square on the left side: (x + 1.9)(x + 1.9) = 20.71 Calculate the square root of the right side: 4.550824101 Break this problem into two subproblems by setting (x + 1.9) equal to 4.550824101 and -4.550824101.Subproblem 1
x + 1.9 = 4.550824101 Simplifying x + 1.9 = 4.550824101 Reorder the terms: 1.9 + x = 4.550824101 Solving 1.9 + x = 4.550824101 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 = 4.550824101 + -1.9 Combine like terms: 1.9 + -1.9 = 0.0 0.0 + x = 4.550824101 + -1.9 x = 4.550824101 + -1.9 Combine like terms: 4.550824101 + -1.9 = 2.650824101 x = 2.650824101 Simplifying x = 2.650824101Subproblem 2
x + 1.9 = -4.550824101 Simplifying x + 1.9 = -4.550824101 Reorder the terms: 1.9 + x = -4.550824101 Solving 1.9 + x = -4.550824101 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 = -4.550824101 + -1.9 Combine like terms: 1.9 + -1.9 = 0.0 0.0 + x = -4.550824101 + -1.9 x = -4.550824101 + -1.9 Combine like terms: -4.550824101 + -1.9 = -6.450824101 x = -6.450824101 Simplifying x = -6.450824101Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.650824101, -6.450824101}
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