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Simplifying x2 + 15x = 65 Reorder the terms: 15x + x2 = 65 Solving 15x + x2 = 65 Solving for variable 'x'. Reorder the terms: -65 + 15x + x2 = 65 + -65 Combine like terms: 65 + -65 = 0 -65 + 15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '65' to each side of the equation. -65 + 15x + 65 + x2 = 0 + 65 Reorder the terms: -65 + 65 + 15x + x2 = 0 + 65 Combine like terms: -65 + 65 = 0 0 + 15x + x2 = 0 + 65 15x + x2 = 0 + 65 Combine like terms: 0 + 65 = 65 15x + x2 = 65 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 = 65 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 65 + 56.25 Combine like terms: 65 + 56.25 = 121.25 56.25 + 15x + x2 = 121.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 121.25 Calculate the square root of the right side: 11.011357773 Break this problem into two subproblems by setting (x + 7.5) equal to 11.011357773 and -11.011357773.Subproblem 1
x + 7.5 = 11.011357773 Simplifying x + 7.5 = 11.011357773 Reorder the terms: 7.5 + x = 11.011357773 Solving 7.5 + x = 11.011357773 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 = 11.011357773 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 11.011357773 + -7.5 x = 11.011357773 + -7.5 Combine like terms: 11.011357773 + -7.5 = 3.511357773 x = 3.511357773 Simplifying x = 3.511357773Subproblem 2
x + 7.5 = -11.011357773 Simplifying x + 7.5 = -11.011357773 Reorder the terms: 7.5 + x = -11.011357773 Solving 7.5 + x = -11.011357773 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 = -11.011357773 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -11.011357773 + -7.5 x = -11.011357773 + -7.5 Combine like terms: -11.011357773 + -7.5 = -18.511357773 x = -18.511357773 Simplifying x = -18.511357773Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.511357773, -18.511357773}
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