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Simplifying 10 + 31x + -4x2 = 0 Solving 10 + 31x + -4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -2.5 + -7.75x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -7.75x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -7.75x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -7.75x + x2 = 0 + 2.5 -7.75x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -7.75x + x2 = 2.5 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 = 2.5 + 15.015625 Reorder the terms: 15.015625 + -7.75x + x2 = 2.5 + 15.015625 Combine like terms: 2.5 + 15.015625 = 17.515625 15.015625 + -7.75x + x2 = 17.515625 Factor a perfect square on the left side: (x + -3.875)(x + -3.875) = 17.515625 Calculate the square root of the right side: 4.185167261 Break this problem into two subproblems by setting (x + -3.875) equal to 4.185167261 and -4.185167261.Subproblem 1
x + -3.875 = 4.185167261 Simplifying x + -3.875 = 4.185167261 Reorder the terms: -3.875 + x = 4.185167261 Solving -3.875 + x = 4.185167261 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 = 4.185167261 + 3.875 Combine like terms: -3.875 + 3.875 = 0.000 0.000 + x = 4.185167261 + 3.875 x = 4.185167261 + 3.875 Combine like terms: 4.185167261 + 3.875 = 8.060167261 x = 8.060167261 Simplifying x = 8.060167261Subproblem 2
x + -3.875 = -4.185167261 Simplifying x + -3.875 = -4.185167261 Reorder the terms: -3.875 + x = -4.185167261 Solving -3.875 + x = -4.185167261 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 = -4.185167261 + 3.875 Combine like terms: -3.875 + 3.875 = 0.000 0.000 + x = -4.185167261 + 3.875 x = -4.185167261 + 3.875 Combine like terms: -4.185167261 + 3.875 = -0.310167261 x = -0.310167261 Simplifying x = -0.310167261Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.060167261, -0.310167261}
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