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Simplifying 0 = x2 + -15x + 17 Reorder the terms: 0 = 17 + -15x + x2 Solving 0 = 17 + -15x + x2 Solving for variable 'x'. Combine like terms: 0 + -17 = -17 -17 + 15x + -1x2 = 17 + -15x + x2 + -17 + 15x + -1x2 Reorder the terms: -17 + 15x + -1x2 = 17 + -17 + -15x + 15x + x2 + -1x2 Combine like terms: 17 + -17 = 0 -17 + 15x + -1x2 = 0 + -15x + 15x + x2 + -1x2 -17 + 15x + -1x2 = -15x + 15x + x2 + -1x2 Combine like terms: -15x + 15x = 0 -17 + 15x + -1x2 = 0 + x2 + -1x2 -17 + 15x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -17 + 15x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 17 + -15x + x2 = 0 Move the constant term to the right: Add '-17' to each side of the equation. 17 + -15x + -17 + x2 = 0 + -17 Reorder the terms: 17 + -17 + -15x + x2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -15x + x2 = 0 + -17 -15x + x2 = 0 + -17 Combine like terms: 0 + -17 = -17 -15x + x2 = -17 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 = -17 + 56.25 Reorder the terms: 56.25 + -15x + x2 = -17 + 56.25 Combine like terms: -17 + 56.25 = 39.25 56.25 + -15x + x2 = 39.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 39.25 Calculate the square root of the right side: 6.264982043 Break this problem into two subproblems by setting (x + -7.5) equal to 6.264982043 and -6.264982043.Subproblem 1
x + -7.5 = 6.264982043 Simplifying x + -7.5 = 6.264982043 Reorder the terms: -7.5 + x = 6.264982043 Solving -7.5 + x = 6.264982043 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 = 6.264982043 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 6.264982043 + 7.5 x = 6.264982043 + 7.5 Combine like terms: 6.264982043 + 7.5 = 13.764982043 x = 13.764982043 Simplifying x = 13.764982043Subproblem 2
x + -7.5 = -6.264982043 Simplifying x + -7.5 = -6.264982043 Reorder the terms: -7.5 + x = -6.264982043 Solving -7.5 + x = -6.264982043 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 = -6.264982043 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -6.264982043 + 7.5 x = -6.264982043 + 7.5 Combine like terms: -6.264982043 + 7.5 = 1.235017957 x = 1.235017957 Simplifying x = 1.235017957Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.764982043, 1.235017957}
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