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Simplifying -4x2 = x + -6 Reorder the terms: -4x2 = -6 + x Solving -4x2 = -6 + x Solving for variable 'x'. Reorder the terms: 6 + -1x + -4x2 = -6 + x + 6 + -1x Reorder the terms: 6 + -1x + -4x2 = -6 + 6 + x + -1x Combine like terms: -6 + 6 = 0 6 + -1x + -4x2 = 0 + x + -1x 6 + -1x + -4x2 = x + -1x Combine like terms: x + -1x = 0 6 + -1x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -1.5 + 0.25x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 0.25x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + 0.25x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 0.25x + x2 = 0 + 1.5 0.25x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 0.25x + x2 = 1.5 The x term is 0.25x. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25x + 0.015625 + x2 = 1.5 + 0.015625 Reorder the terms: 0.015625 + 0.25x + x2 = 1.5 + 0.015625 Combine like terms: 1.5 + 0.015625 = 1.515625 0.015625 + 0.25x + x2 = 1.515625 Factor a perfect square on the left side: (x + 0.125)(x + 0.125) = 1.515625 Calculate the square root of the right side: 1.231107225 Break this problem into two subproblems by setting (x + 0.125) equal to 1.231107225 and -1.231107225.Subproblem 1
x + 0.125 = 1.231107225 Simplifying x + 0.125 = 1.231107225 Reorder the terms: 0.125 + x = 1.231107225 Solving 0.125 + x = 1.231107225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = 1.231107225 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = 1.231107225 + -0.125 x = 1.231107225 + -0.125 Combine like terms: 1.231107225 + -0.125 = 1.106107225 x = 1.106107225 Simplifying x = 1.106107225Subproblem 2
x + 0.125 = -1.231107225 Simplifying x + 0.125 = -1.231107225 Reorder the terms: 0.125 + x = -1.231107225 Solving 0.125 + x = -1.231107225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = -1.231107225 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = -1.231107225 + -0.125 x = -1.231107225 + -0.125 Combine like terms: -1.231107225 + -0.125 = -1.356107225 x = -1.356107225 Simplifying x = -1.356107225Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.106107225, -1.356107225}
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