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Simplifying x2 + -272x + 960 = 0 Reorder the terms: 960 + -272x + x2 = 0 Solving 960 + -272x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-960' to each side of the equation. 960 + -272x + -960 + x2 = 0 + -960 Reorder the terms: 960 + -960 + -272x + x2 = 0 + -960 Combine like terms: 960 + -960 = 0 0 + -272x + x2 = 0 + -960 -272x + x2 = 0 + -960 Combine like terms: 0 + -960 = -960 -272x + x2 = -960 The x term is -272x. Take half its coefficient (-136). Square it (18496) and add it to both sides. Add '18496' to each side of the equation. -272x + 18496 + x2 = -960 + 18496 Reorder the terms: 18496 + -272x + x2 = -960 + 18496 Combine like terms: -960 + 18496 = 17536 18496 + -272x + x2 = 17536 Factor a perfect square on the left side: (x + -136)(x + -136) = 17536 Calculate the square root of the right side: 132.423562858 Break this problem into two subproblems by setting (x + -136) equal to 132.423562858 and -132.423562858.Subproblem 1
x + -136 = 132.423562858 Simplifying x + -136 = 132.423562858 Reorder the terms: -136 + x = 132.423562858 Solving -136 + x = 132.423562858 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '136' to each side of the equation. -136 + 136 + x = 132.423562858 + 136 Combine like terms: -136 + 136 = 0 0 + x = 132.423562858 + 136 x = 132.423562858 + 136 Combine like terms: 132.423562858 + 136 = 268.423562858 x = 268.423562858 Simplifying x = 268.423562858Subproblem 2
x + -136 = -132.423562858 Simplifying x + -136 = -132.423562858 Reorder the terms: -136 + x = -132.423562858 Solving -136 + x = -132.423562858 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '136' to each side of the equation. -136 + 136 + x = -132.423562858 + 136 Combine like terms: -136 + 136 = 0 0 + x = -132.423562858 + 136 x = -132.423562858 + 136 Combine like terms: -132.423562858 + 136 = 3.576437142 x = 3.576437142 Simplifying x = 3.576437142Solution
The solution to the problem is based on the solutions from the subproblems. x = {268.423562858, 3.576437142}
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