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Simplifying 4x2 = 3.08 + -1.54x Solving 4x2 = 3.08 + -1.54x Solving for variable 'x'. Reorder the terms: -3.08 + 1.54x + 4x2 = 3.08 + -1.54x + -3.08 + 1.54x Reorder the terms: -3.08 + 1.54x + 4x2 = 3.08 + -3.08 + -1.54x + 1.54x Combine like terms: 3.08 + -3.08 = 0.00 -3.08 + 1.54x + 4x2 = 0.00 + -1.54x + 1.54x -3.08 + 1.54x + 4x2 = -1.54x + 1.54x Combine like terms: -1.54x + 1.54x = 0.00 -3.08 + 1.54x + 4x2 = 0.00 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.77 + 0.385x + x2 = 0.00 Move the constant term to the right: Add '0.77' to each side of the equation. -0.77 + 0.385x + 0.77 + x2 = 0.00 + 0.77 Reorder the terms: -0.77 + 0.77 + 0.385x + x2 = 0.00 + 0.77 Combine like terms: -0.77 + 0.77 = 0.00 0.00 + 0.385x + x2 = 0.00 + 0.77 0.385x + x2 = 0.00 + 0.77 Combine like terms: 0.00 + 0.77 = 0.77 0.385x + x2 = 0.77 The x term is 0.385x. Take half its coefficient (0.1925). Square it (0.03705625) and add it to both sides. Add '0.03705625' to each side of the equation. 0.385x + 0.03705625 + x2 = 0.77 + 0.03705625 Reorder the terms: 0.03705625 + 0.385x + x2 = 0.77 + 0.03705625 Combine like terms: 0.77 + 0.03705625 = 0.80705625 0.03705625 + 0.385x + x2 = 0.80705625 Factor a perfect square on the left side: (x + 0.1925)(x + 0.1925) = 0.80705625 Calculate the square root of the right side: 0.898363095 Break this problem into two subproblems by setting (x + 0.1925) equal to 0.898363095 and -0.898363095.Subproblem 1
x + 0.1925 = 0.898363095 Simplifying x + 0.1925 = 0.898363095 Reorder the terms: 0.1925 + x = 0.898363095 Solving 0.1925 + x = 0.898363095 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1925' to each side of the equation. 0.1925 + -0.1925 + x = 0.898363095 + -0.1925 Combine like terms: 0.1925 + -0.1925 = 0.0000 0.0000 + x = 0.898363095 + -0.1925 x = 0.898363095 + -0.1925 Combine like terms: 0.898363095 + -0.1925 = 0.705863095 x = 0.705863095 Simplifying x = 0.705863095Subproblem 2
x + 0.1925 = -0.898363095 Simplifying x + 0.1925 = -0.898363095 Reorder the terms: 0.1925 + x = -0.898363095 Solving 0.1925 + x = -0.898363095 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1925' to each side of the equation. 0.1925 + -0.1925 + x = -0.898363095 + -0.1925 Combine like terms: 0.1925 + -0.1925 = 0.0000 0.0000 + x = -0.898363095 + -0.1925 x = -0.898363095 + -0.1925 Combine like terms: -0.898363095 + -0.1925 = -1.090863095 x = -1.090863095 Simplifying x = -1.090863095Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.705863095, -1.090863095}
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