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Simplifying 0.04x2 + 1.1x + -2 = 0 Reorder the terms: -2 + 1.1x + 0.04x2 = 0 Solving -2 + 1.1x + 0.04x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.04 the coefficient of the squared term: Divide each side by '0.04'. -50 + 27.5x + x2 = 0 Move the constant term to the right: Add '50' to each side of the equation. -50 + 27.5x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + 27.5x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 27.5x + x2 = 0 + 50 27.5x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 27.5x + x2 = 50 The x term is 27.5x. Take half its coefficient (13.75). Square it (189.0625) and add it to both sides. Add '189.0625' to each side of the equation. 27.5x + 189.0625 + x2 = 50 + 189.0625 Reorder the terms: 189.0625 + 27.5x + x2 = 50 + 189.0625 Combine like terms: 50 + 189.0625 = 239.0625 189.0625 + 27.5x + x2 = 239.0625 Factor a perfect square on the left side: (x + 13.75)(x + 13.75) = 239.0625 Calculate the square root of the right side: 15.461646096 Break this problem into two subproblems by setting (x + 13.75) equal to 15.461646096 and -15.461646096.Subproblem 1
x + 13.75 = 15.461646096 Simplifying x + 13.75 = 15.461646096 Reorder the terms: 13.75 + x = 15.461646096 Solving 13.75 + x = 15.461646096 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.75' to each side of the equation. 13.75 + -13.75 + x = 15.461646096 + -13.75 Combine like terms: 13.75 + -13.75 = 0.00 0.00 + x = 15.461646096 + -13.75 x = 15.461646096 + -13.75 Combine like terms: 15.461646096 + -13.75 = 1.711646096 x = 1.711646096 Simplifying x = 1.711646096Subproblem 2
x + 13.75 = -15.461646096 Simplifying x + 13.75 = -15.461646096 Reorder the terms: 13.75 + x = -15.461646096 Solving 13.75 + x = -15.461646096 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.75' to each side of the equation. 13.75 + -13.75 + x = -15.461646096 + -13.75 Combine like terms: 13.75 + -13.75 = 0.00 0.00 + x = -15.461646096 + -13.75 x = -15.461646096 + -13.75 Combine like terms: -15.461646096 + -13.75 = -29.211646096 x = -29.211646096 Simplifying x = -29.211646096Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.711646096, -29.211646096}
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