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Simplifying 4x2 + -12x + -31 = 0 Reorder the terms: -31 + -12x + 4x2 = 0 Solving -31 + -12x + 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'. -7.75 + -3x + x2 = 0 Move the constant term to the right: Add '7.75' to each side of the equation. -7.75 + -3x + 7.75 + x2 = 0 + 7.75 Reorder the terms: -7.75 + 7.75 + -3x + x2 = 0 + 7.75 Combine like terms: -7.75 + 7.75 = 0.00 0.00 + -3x + x2 = 0 + 7.75 -3x + x2 = 0 + 7.75 Combine like terms: 0 + 7.75 = 7.75 -3x + x2 = 7.75 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 7.75 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 7.75 + 2.25 Combine like terms: 7.75 + 2.25 = 10 2.25 + -3x + x2 = 10 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (x + -1.5) equal to 3.16227766 and -3.16227766.Subproblem 1
x + -1.5 = 3.16227766 Simplifying x + -1.5 = 3.16227766 Reorder the terms: -1.5 + x = 3.16227766 Solving -1.5 + x = 3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 3.16227766 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 3.16227766 + 1.5 x = 3.16227766 + 1.5 Combine like terms: 3.16227766 + 1.5 = 4.66227766 x = 4.66227766 Simplifying x = 4.66227766Subproblem 2
x + -1.5 = -3.16227766 Simplifying x + -1.5 = -3.16227766 Reorder the terms: -1.5 + x = -3.16227766 Solving -1.5 + x = -3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -3.16227766 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -3.16227766 + 1.5 x = -3.16227766 + 1.5 Combine like terms: -3.16227766 + 1.5 = -1.66227766 x = -1.66227766 Simplifying x = -1.66227766Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.66227766, -1.66227766}
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