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Simplifying 4x2 + -31x + -8 = 9 Reorder the terms: -8 + -31x + 4x2 = 9 Solving -8 + -31x + 4x2 = 9 Solving for variable 'x'. Reorder the terms: -8 + -9 + -31x + 4x2 = 9 + -9 Combine like terms: -8 + -9 = -17 -17 + -31x + 4x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -17 + -31x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -4.25 + -7.75x + x2 = 0 Move the constant term to the right: Add '4.25' to each side of the equation. -4.25 + -7.75x + 4.25 + x2 = 0 + 4.25 Reorder the terms: -4.25 + 4.25 + -7.75x + x2 = 0 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + -7.75x + x2 = 0 + 4.25 -7.75x + x2 = 0 + 4.25 Combine like terms: 0 + 4.25 = 4.25 -7.75x + x2 = 4.25 The x term is -7.75x. Take half its coefficient (-3.875). Square it (15.015625) and add it to both sides. Add '15.015625' to each side of the equation. -7.75x + 15.015625 + x2 = 4.25 + 15.015625 Reorder the terms: 15.015625 + -7.75x + x2 = 4.25 + 15.015625 Combine like terms: 4.25 + 15.015625 = 19.265625 15.015625 + -7.75x + x2 = 19.265625 Factor a perfect square on the left side: (x + -3.875)(x + -3.875) = 19.265625 Calculate the square root of the right side: 4.389262467 Break this problem into two subproblems by setting (x + -3.875) equal to 4.389262467 and -4.389262467.Subproblem 1
x + -3.875 = 4.389262467 Simplifying x + -3.875 = 4.389262467 Reorder the terms: -3.875 + x = 4.389262467 Solving -3.875 + x = 4.389262467 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.875' to each side of the equation. -3.875 + 3.875 + x = 4.389262467 + 3.875 Combine like terms: -3.875 + 3.875 = 0.000 0.000 + x = 4.389262467 + 3.875 x = 4.389262467 + 3.875 Combine like terms: 4.389262467 + 3.875 = 8.264262467 x = 8.264262467 Simplifying x = 8.264262467Subproblem 2
x + -3.875 = -4.389262467 Simplifying x + -3.875 = -4.389262467 Reorder the terms: -3.875 + x = -4.389262467 Solving -3.875 + x = -4.389262467 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.875' to each side of the equation. -3.875 + 3.875 + x = -4.389262467 + 3.875 Combine like terms: -3.875 + 3.875 = 0.000 0.000 + x = -4.389262467 + 3.875 x = -4.389262467 + 3.875 Combine like terms: -4.389262467 + 3.875 = -0.514262467 x = -0.514262467 Simplifying x = -0.514262467Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.264262467, -0.514262467}
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