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Simplifying (2x * x) + -8x = 3 Multiply x * x (2x2) + -8x = 3 Reorder the terms: -8x + (2x2) = 3 Solving -8x + (2x2) = 3 Solving for variable 'x'. Reorder the terms: -3 + -8x + (2x2) = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + -8x + (2x2) = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1.5 + -4x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -4x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -4x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -4x + x2 = 0 + 1.5 -4x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -4x + x2 = 1.5 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 1.5 + 4 Reorder the terms: 4 + -4x + x2 = 1.5 + 4 Combine like terms: 1.5 + 4 = 5.5 4 + -4x + x2 = 5.5 Factor a perfect square on the left side: ((x) + -2)((x) + -2) = 5.5 Calculate the square root of the right side: 2.34520788 Break this problem into two subproblems by setting ((x) + -2) equal to 2.34520788 and -2.34520788.Subproblem 1
(x) + -2 = 2.34520788 Simplifying (x) + -2 = 2.34520788 x + -2 = 2.34520788 Reorder the terms: -2 + x = 2.34520788 Solving -2 + x = 2.34520788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 2.34520788 + 2 Combine like terms: -2 + 2 = 0 0 + x = 2.34520788 + 2 x = 2.34520788 + 2 Combine like terms: 2.34520788 + 2 = 4.34520788 x = 4.34520788 Simplifying x = 4.34520788Subproblem 2
(x) + -2 = -2.34520788 Simplifying (x) + -2 = -2.34520788 x + -2 = -2.34520788 Reorder the terms: -2 + x = -2.34520788 Solving -2 + x = -2.34520788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -2.34520788 + 2 Combine like terms: -2 + 2 = 0 0 + x = -2.34520788 + 2 x = -2.34520788 + 2 Combine like terms: -2.34520788 + 2 = -0.34520788 x = -0.34520788 Simplifying x = -0.34520788Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.34520788, -0.34520788}
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