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Simplifying 8x2 + -35x + -38 = 0 Reorder the terms: -38 + -35x + 8x2 = 0 Solving -38 + -35x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -4.75 + -4.375x + x2 = 0 Move the constant term to the right: Add '4.75' to each side of the equation. -4.75 + -4.375x + 4.75 + x2 = 0 + 4.75 Reorder the terms: -4.75 + 4.75 + -4.375x + x2 = 0 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + -4.375x + x2 = 0 + 4.75 -4.375x + x2 = 0 + 4.75 Combine like terms: 0 + 4.75 = 4.75 -4.375x + x2 = 4.75 The x term is -4.375x. Take half its coefficient (-2.1875). Square it (4.78515625) and add it to both sides. Add '4.78515625' to each side of the equation. -4.375x + 4.78515625 + x2 = 4.75 + 4.78515625 Reorder the terms: 4.78515625 + -4.375x + x2 = 4.75 + 4.78515625 Combine like terms: 4.75 + 4.78515625 = 9.53515625 4.78515625 + -4.375x + x2 = 9.53515625 Factor a perfect square on the left side: (x + -2.1875)(x + -2.1875) = 9.53515625 Calculate the square root of the right side: 3.087904832 Break this problem into two subproblems by setting (x + -2.1875) equal to 3.087904832 and -3.087904832.Subproblem 1
x + -2.1875 = 3.087904832 Simplifying x + -2.1875 = 3.087904832 Reorder the terms: -2.1875 + x = 3.087904832 Solving -2.1875 + x = 3.087904832 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.1875' to each side of the equation. -2.1875 + 2.1875 + x = 3.087904832 + 2.1875 Combine like terms: -2.1875 + 2.1875 = 0.0000 0.0000 + x = 3.087904832 + 2.1875 x = 3.087904832 + 2.1875 Combine like terms: 3.087904832 + 2.1875 = 5.275404832 x = 5.275404832 Simplifying x = 5.275404832Subproblem 2
x + -2.1875 = -3.087904832 Simplifying x + -2.1875 = -3.087904832 Reorder the terms: -2.1875 + x = -3.087904832 Solving -2.1875 + x = -3.087904832 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.1875' to each side of the equation. -2.1875 + 2.1875 + x = -3.087904832 + 2.1875 Combine like terms: -2.1875 + 2.1875 = 0.0000 0.0000 + x = -3.087904832 + 2.1875 x = -3.087904832 + 2.1875 Combine like terms: -3.087904832 + 2.1875 = -0.900404832 x = -0.900404832 Simplifying x = -0.900404832Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.275404832, -0.900404832}
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