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Simplifying x2 + 10x = 65.25 Reorder the terms: 10x + x2 = 65.25 Solving 10x + x2 = 65.25 Solving for variable 'x'. Reorder the terms: -65.25 + 10x + x2 = 65.25 + -65.25 Combine like terms: 65.25 + -65.25 = 0.00 -65.25 + 10x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '65.25' to each side of the equation. -65.25 + 10x + 65.25 + x2 = 0.00 + 65.25 Reorder the terms: -65.25 + 65.25 + 10x + x2 = 0.00 + 65.25 Combine like terms: -65.25 + 65.25 = 0.00 0.00 + 10x + x2 = 0.00 + 65.25 10x + x2 = 0.00 + 65.25 Combine like terms: 0.00 + 65.25 = 65.25 10x + x2 = 65.25 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 65.25 + 25 Reorder the terms: 25 + 10x + x2 = 65.25 + 25 Combine like terms: 65.25 + 25 = 90.25 25 + 10x + x2 = 90.25 Factor a perfect square on the left side: (x + 5)(x + 5) = 90.25 Calculate the square root of the right side: 9.5 Break this problem into two subproblems by setting (x + 5) equal to 9.5 and -9.5.Subproblem 1
x + 5 = 9.5 Simplifying x + 5 = 9.5 Reorder the terms: 5 + x = 9.5 Solving 5 + x = 9.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 9.5 + -5 Combine like terms: 5 + -5 = 0 0 + x = 9.5 + -5 x = 9.5 + -5 Combine like terms: 9.5 + -5 = 4.5 x = 4.5 Simplifying x = 4.5Subproblem 2
x + 5 = -9.5 Simplifying x + 5 = -9.5 Reorder the terms: 5 + x = -9.5 Solving 5 + x = -9.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -9.5 + -5 Combine like terms: 5 + -5 = 0 0 + x = -9.5 + -5 x = -9.5 + -5 Combine like terms: -9.5 + -5 = -14.5 x = -14.5 Simplifying x = -14.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.5, -14.5}
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