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Simplifying 0 = 2600 + 15x + -1x2 Solving 0 = 2600 + 15x + -1x2 Solving for variable 'x'. Combine like terms: 0 + -2600 = -2600 -2600 + -15x + x2 = 2600 + 15x + -1x2 + -2600 + -15x + x2 Reorder the terms: -2600 + -15x + x2 = 2600 + -2600 + 15x + -15x + -1x2 + x2 Combine like terms: 2600 + -2600 = 0 -2600 + -15x + x2 = 0 + 15x + -15x + -1x2 + x2 -2600 + -15x + x2 = 15x + -15x + -1x2 + x2 Combine like terms: 15x + -15x = 0 -2600 + -15x + x2 = 0 + -1x2 + x2 -2600 + -15x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -2600 + -15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2600' to each side of the equation. -2600 + -15x + 2600 + x2 = 0 + 2600 Reorder the terms: -2600 + 2600 + -15x + x2 = 0 + 2600 Combine like terms: -2600 + 2600 = 0 0 + -15x + x2 = 0 + 2600 -15x + x2 = 0 + 2600 Combine like terms: 0 + 2600 = 2600 -15x + x2 = 2600 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = 2600 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 2600 + 56.25 Combine like terms: 2600 + 56.25 = 2656.25 56.25 + -15x + x2 = 2656.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 2656.25 Calculate the square root of the right side: 51.53882032 Break this problem into two subproblems by setting (x + -7.5) equal to 51.53882032 and -51.53882032.Subproblem 1
x + -7.5 = 51.53882032 Simplifying x + -7.5 = 51.53882032 Reorder the terms: -7.5 + x = 51.53882032 Solving -7.5 + x = 51.53882032 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 51.53882032 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 51.53882032 + 7.5 x = 51.53882032 + 7.5 Combine like terms: 51.53882032 + 7.5 = 59.03882032 x = 59.03882032 Simplifying x = 59.03882032Subproblem 2
x + -7.5 = -51.53882032 Simplifying x + -7.5 = -51.53882032 Reorder the terms: -7.5 + x = -51.53882032 Solving -7.5 + x = -51.53882032 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -51.53882032 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -51.53882032 + 7.5 x = -51.53882032 + 7.5 Combine like terms: -51.53882032 + 7.5 = -44.03882032 x = -44.03882032 Simplifying x = -44.03882032Solution
The solution to the problem is based on the solutions from the subproblems. x = {59.03882032, -44.03882032}
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