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Simplifying 2x2 + -2 = -0.5x + 4 Reorder the terms: -2 + 2x2 = -0.5x + 4 Reorder the terms: -2 + 2x2 = 4 + -0.5x Solving -2 + 2x2 = 4 + -0.5x Solving for variable 'x'. Reorder the terms: -2 + -4 + 0.5x + 2x2 = 4 + -0.5x + -4 + 0.5x Combine like terms: -2 + -4 = -6 -6 + 0.5x + 2x2 = 4 + -0.5x + -4 + 0.5x Reorder the terms: -6 + 0.5x + 2x2 = 4 + -4 + -0.5x + 0.5x Combine like terms: 4 + -4 = 0 -6 + 0.5x + 2x2 = 0 + -0.5x + 0.5x -6 + 0.5x + 2x2 = -0.5x + 0.5x Combine like terms: -0.5x + 0.5x = 0.0 -6 + 0.5x + 2x2 = 0.0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3 + 0.25x + x2 = 0.0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 0.25x + 3 + x2 = 0.0 + 3 Reorder the terms: -3 + 3 + 0.25x + x2 = 0.0 + 3 Combine like terms: -3 + 3 = 0 0 + 0.25x + x2 = 0.0 + 3 0.25x + x2 = 0.0 + 3 Combine like terms: 0.0 + 3 = 3 0.25x + x2 = 3 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 = 3 + 0.015625 Reorder the terms: 0.015625 + 0.25x + x2 = 3 + 0.015625 Combine like terms: 3 + 0.015625 = 3.015625 0.015625 + 0.25x + x2 = 3.015625 Factor a perfect square on the left side: (x + 0.125)(x + 0.125) = 3.015625 Calculate the square root of the right side: 1.736555499 Break this problem into two subproblems by setting (x + 0.125) equal to 1.736555499 and -1.736555499.Subproblem 1
x + 0.125 = 1.736555499 Simplifying x + 0.125 = 1.736555499 Reorder the terms: 0.125 + x = 1.736555499 Solving 0.125 + x = 1.736555499 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 = 1.736555499 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = 1.736555499 + -0.125 x = 1.736555499 + -0.125 Combine like terms: 1.736555499 + -0.125 = 1.611555499 x = 1.611555499 Simplifying x = 1.611555499Subproblem 2
x + 0.125 = -1.736555499 Simplifying x + 0.125 = -1.736555499 Reorder the terms: 0.125 + x = -1.736555499 Solving 0.125 + x = -1.736555499 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 = -1.736555499 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = -1.736555499 + -0.125 x = -1.736555499 + -0.125 Combine like terms: -1.736555499 + -0.125 = -1.861555499 x = -1.861555499 Simplifying x = -1.861555499Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.611555499, -1.861555499}
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