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Simplifying 4x2 + 36x + -31 = 0 Reorder the terms: -31 + 36x + 4x2 = 0 Solving -31 + 36x + 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 + 9x + x2 = 0 Move the constant term to the right: Add '7.75' to each side of the equation. -7.75 + 9x + 7.75 + x2 = 0 + 7.75 Reorder the terms: -7.75 + 7.75 + 9x + x2 = 0 + 7.75 Combine like terms: -7.75 + 7.75 = 0.00 0.00 + 9x + x2 = 0 + 7.75 9x + x2 = 0 + 7.75 Combine like terms: 0 + 7.75 = 7.75 9x + x2 = 7.75 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 7.75 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 7.75 + 20.25 Combine like terms: 7.75 + 20.25 = 28 20.25 + 9x + x2 = 28 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (x + 4.5) equal to 5.291502622 and -5.291502622.Subproblem 1
x + 4.5 = 5.291502622 Simplifying x + 4.5 = 5.291502622 Reorder the terms: 4.5 + x = 5.291502622 Solving 4.5 + x = 5.291502622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 5.291502622 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 5.291502622 + -4.5 x = 5.291502622 + -4.5 Combine like terms: 5.291502622 + -4.5 = 0.791502622 x = 0.791502622 Simplifying x = 0.791502622Subproblem 2
x + 4.5 = -5.291502622 Simplifying x + 4.5 = -5.291502622 Reorder the terms: 4.5 + x = -5.291502622 Solving 4.5 + x = -5.291502622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -5.291502622 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -5.291502622 + -4.5 x = -5.291502622 + -4.5 Combine like terms: -5.291502622 + -4.5 = -9.791502622 x = -9.791502622 Simplifying x = -9.791502622Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.791502622, -9.791502622}
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