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Simplifying 0 = 72 + -2x2 + x Reorder the terms: 0 = 72 + x + -2x2 Solving 0 = 72 + x + -2x2 Solving for variable 'x'. Combine like terms: 0 + -72 = -72 -72 + -1x + 2x2 = 72 + x + -2x2 + -72 + -1x + 2x2 Reorder the terms: -72 + -1x + 2x2 = 72 + -72 + x + -1x + -2x2 + 2x2 Combine like terms: 72 + -72 = 0 -72 + -1x + 2x2 = 0 + x + -1x + -2x2 + 2x2 -72 + -1x + 2x2 = x + -1x + -2x2 + 2x2 Combine like terms: x + -1x = 0 -72 + -1x + 2x2 = 0 + -2x2 + 2x2 -72 + -1x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -72 + -1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -36 + -0.5x + x2 = 0 Move the constant term to the right: Add '36' to each side of the equation. -36 + -0.5x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + -0.5x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -0.5x + x2 = 0 + 36 -0.5x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 -0.5x + x2 = 36 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 36 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 36 + 0.0625 Combine like terms: 36 + 0.0625 = 36.0625 0.0625 + -0.5x + x2 = 36.0625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 36.0625 Calculate the square root of the right side: 6.005206075 Break this problem into two subproblems by setting (x + -0.25) equal to 6.005206075 and -6.005206075.Subproblem 1
x + -0.25 = 6.005206075 Simplifying x + -0.25 = 6.005206075 Reorder the terms: -0.25 + x = 6.005206075 Solving -0.25 + x = 6.005206075 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 6.005206075 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 6.005206075 + 0.25 x = 6.005206075 + 0.25 Combine like terms: 6.005206075 + 0.25 = 6.255206075 x = 6.255206075 Simplifying x = 6.255206075Subproblem 2
x + -0.25 = -6.005206075 Simplifying x + -0.25 = -6.005206075 Reorder the terms: -0.25 + x = -6.005206075 Solving -0.25 + x = -6.005206075 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -6.005206075 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -6.005206075 + 0.25 x = -6.005206075 + 0.25 Combine like terms: -6.005206075 + 0.25 = -5.755206075 x = -5.755206075 Simplifying x = -5.755206075Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.255206075, -5.755206075}
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