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Simplifying 8x2 + -7x + -38 = x Reorder the terms: -38 + -7x + 8x2 = x Solving -38 + -7x + 8x2 = x Solving for variable 'x'. Reorder the terms: -38 + -7x + -1x + 8x2 = x + -1x Combine like terms: -7x + -1x = -8x -38 + -8x + 8x2 = x + -1x Combine like terms: x + -1x = 0 -38 + -8x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-19 + -4x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-19 + -4x + 4x2)' equal to zero and attempt to solve: Simplifying -19 + -4x + 4x2 = 0 Solving -19 + -4x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -4.75 + -1x + x2 = 0 Move the constant term to the right: Add '4.75' to each side of the equation. -4.75 + -1x + 4.75 + x2 = 0 + 4.75 Reorder the terms: -4.75 + 4.75 + -1x + x2 = 0 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + -1x + x2 = 0 + 4.75 -1x + x2 = 0 + 4.75 Combine like terms: 0 + 4.75 = 4.75 -1x + x2 = 4.75 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 4.75 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 4.75 + 0.25 Combine like terms: 4.75 + 0.25 = 5 0.25 + -1x + x2 = 5 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (x + -0.5) equal to 2.236067978 and -2.236067978.Subproblem 1
x + -0.5 = 2.236067978 Simplifying x + -0.5 = 2.236067978 Reorder the terms: -0.5 + x = 2.236067978 Solving -0.5 + x = 2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 2.236067978 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 2.236067978 + 0.5 x = 2.236067978 + 0.5 Combine like terms: 2.236067978 + 0.5 = 2.736067978 x = 2.736067978 Simplifying x = 2.736067978Subproblem 2
x + -0.5 = -2.236067978 Simplifying x + -0.5 = -2.236067978 Reorder the terms: -0.5 + x = -2.236067978 Solving -0.5 + x = -2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -2.236067978 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -2.236067978 + 0.5 x = -2.236067978 + 0.5 Combine like terms: -2.236067978 + 0.5 = -1.736067978 x = -1.736067978 Simplifying x = -1.736067978Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.736067978, -1.736067978}Solution
x = {2.736067978, -1.736067978}
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