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Simplifying x2 + 10x + 25 = 95 Reorder the terms: 25 + 10x + x2 = 95 Solving 25 + 10x + x2 = 95 Solving for variable 'x'. Reorder the terms: 25 + -95 + 10x + x2 = 95 + -95 Combine like terms: 25 + -95 = -70 -70 + 10x + x2 = 95 + -95 Combine like terms: 95 + -95 = 0 -70 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '70' to each side of the equation. -70 + 10x + 70 + x2 = 0 + 70 Reorder the terms: -70 + 70 + 10x + x2 = 0 + 70 Combine like terms: -70 + 70 = 0 0 + 10x + x2 = 0 + 70 10x + x2 = 0 + 70 Combine like terms: 0 + 70 = 70 10x + x2 = 70 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 = 70 + 25 Reorder the terms: 25 + 10x + x2 = 70 + 25 Combine like terms: 70 + 25 = 95 25 + 10x + x2 = 95 Factor a perfect square on the left side: (x + 5)(x + 5) = 95 Calculate the square root of the right side: 9.746794345 Break this problem into two subproblems by setting (x + 5) equal to 9.746794345 and -9.746794345.Subproblem 1
x + 5 = 9.746794345 Simplifying x + 5 = 9.746794345 Reorder the terms: 5 + x = 9.746794345 Solving 5 + x = 9.746794345 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 = 9.746794345 + -5 Combine like terms: 5 + -5 = 0 0 + x = 9.746794345 + -5 x = 9.746794345 + -5 Combine like terms: 9.746794345 + -5 = 4.746794345 x = 4.746794345 Simplifying x = 4.746794345Subproblem 2
x + 5 = -9.746794345 Simplifying x + 5 = -9.746794345 Reorder the terms: 5 + x = -9.746794345 Solving 5 + x = -9.746794345 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 = -9.746794345 + -5 Combine like terms: 5 + -5 = 0 0 + x = -9.746794345 + -5 x = -9.746794345 + -5 Combine like terms: -9.746794345 + -5 = -14.746794345 x = -14.746794345 Simplifying x = -14.746794345Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.746794345, -14.746794345}
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