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Simplifying (x2) + -1(5x) + -57 = 0 x2 + -1(5x) + -57 = 0 Remove parenthesis around (5x) x2 + -1 * 5x + -57 = 0 Multiply -1 * 5 x2 + -5x + -57 = 0 Reorder the terms: -57 + -5x + x2 = 0 Solving -57 + -5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '57' to each side of the equation. -57 + -5x + 57 + x2 = 0 + 57 Reorder the terms: -57 + 57 + -5x + x2 = 0 + 57 Combine like terms: -57 + 57 = 0 0 + -5x + x2 = 0 + 57 -5x + x2 = 0 + 57 Combine like terms: 0 + 57 = 57 -5x + x2 = 57 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 57 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 57 + 6.25 Combine like terms: 57 + 6.25 = 63.25 6.25 + -5x + x2 = 63.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 63.25 Calculate the square root of the right side: 7.95298686 Break this problem into two subproblems by setting (x + -2.5) equal to 7.95298686 and -7.95298686.Subproblem 1
x + -2.5 = 7.95298686 Simplifying x + -2.5 = 7.95298686 Reorder the terms: -2.5 + x = 7.95298686 Solving -2.5 + x = 7.95298686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 7.95298686 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 7.95298686 + 2.5 x = 7.95298686 + 2.5 Combine like terms: 7.95298686 + 2.5 = 10.45298686 x = 10.45298686 Simplifying x = 10.45298686Subproblem 2
x + -2.5 = -7.95298686 Simplifying x + -2.5 = -7.95298686 Reorder the terms: -2.5 + x = -7.95298686 Solving -2.5 + x = -7.95298686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -7.95298686 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -7.95298686 + 2.5 x = -7.95298686 + 2.5 Combine like terms: -7.95298686 + 2.5 = -5.45298686 x = -5.45298686 Simplifying x = -5.45298686Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.45298686, -5.45298686}
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