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Simplifying x2 + 1.67x + -19.02 = 0 Reorder the terms: -19.02 + 1.67x + x2 = 0 Solving -19.02 + 1.67x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '19.02' to each side of the equation. -19.02 + 1.67x + 19.02 + x2 = 0 + 19.02 Reorder the terms: -19.02 + 19.02 + 1.67x + x2 = 0 + 19.02 Combine like terms: -19.02 + 19.02 = 0.00 0.00 + 1.67x + x2 = 0 + 19.02 1.67x + x2 = 0 + 19.02 Combine like terms: 0 + 19.02 = 19.02 1.67x + x2 = 19.02 The x term is 1.67x. Take half its coefficient (0.835). Square it (0.697225) and add it to both sides. Add '0.697225' to each side of the equation. 1.67x + 0.697225 + x2 = 19.02 + 0.697225 Reorder the terms: 0.697225 + 1.67x + x2 = 19.02 + 0.697225 Combine like terms: 19.02 + 0.697225 = 19.717225 0.697225 + 1.67x + x2 = 19.717225 Factor a perfect square on the left side: (x + 0.835)(x + 0.835) = 19.717225 Calculate the square root of the right side: 4.440408202 Break this problem into two subproblems by setting (x + 0.835) equal to 4.440408202 and -4.440408202.Subproblem 1
x + 0.835 = 4.440408202 Simplifying x + 0.835 = 4.440408202 Reorder the terms: 0.835 + x = 4.440408202 Solving 0.835 + x = 4.440408202 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.835' to each side of the equation. 0.835 + -0.835 + x = 4.440408202 + -0.835 Combine like terms: 0.835 + -0.835 = 0.000 0.000 + x = 4.440408202 + -0.835 x = 4.440408202 + -0.835 Combine like terms: 4.440408202 + -0.835 = 3.605408202 x = 3.605408202 Simplifying x = 3.605408202Subproblem 2
x + 0.835 = -4.440408202 Simplifying x + 0.835 = -4.440408202 Reorder the terms: 0.835 + x = -4.440408202 Solving 0.835 + x = -4.440408202 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.835' to each side of the equation. 0.835 + -0.835 + x = -4.440408202 + -0.835 Combine like terms: 0.835 + -0.835 = 0.000 0.000 + x = -4.440408202 + -0.835 x = -4.440408202 + -0.835 Combine like terms: -4.440408202 + -0.835 = -5.275408202 x = -5.275408202 Simplifying x = -5.275408202Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.605408202, -5.275408202}
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