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Simplifying x2 + 10x + 25 = 0.64 Reorder the terms: 25 + 10x + x2 = 0.64 Solving 25 + 10x + x2 = 0.64 Solving for variable 'x'. Reorder the terms: 25 + -0.64 + 10x + x2 = 0.64 + -0.64 Combine like terms: 25 + -0.64 = 24.36 24.36 + 10x + x2 = 0.64 + -0.64 Combine like terms: 0.64 + -0.64 = 0.00 24.36 + 10x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '-24.36' to each side of the equation. 24.36 + 10x + -24.36 + x2 = 0.00 + -24.36 Reorder the terms: 24.36 + -24.36 + 10x + x2 = 0.00 + -24.36 Combine like terms: 24.36 + -24.36 = 0.00 0.00 + 10x + x2 = 0.00 + -24.36 10x + x2 = 0.00 + -24.36 Combine like terms: 0.00 + -24.36 = -24.36 10x + x2 = -24.36 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 = -24.36 + 25 Reorder the terms: 25 + 10x + x2 = -24.36 + 25 Combine like terms: -24.36 + 25 = 0.64 25 + 10x + x2 = 0.64 Factor a perfect square on the left side: (x + 5)(x + 5) = 0.64 Calculate the square root of the right side: 0.8 Break this problem into two subproblems by setting (x + 5) equal to 0.8 and -0.8.Subproblem 1
x + 5 = 0.8 Simplifying x + 5 = 0.8 Reorder the terms: 5 + x = 0.8 Solving 5 + x = 0.8 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 = 0.8 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0.8 + -5 x = 0.8 + -5 Combine like terms: 0.8 + -5 = -4.2 x = -4.2 Simplifying x = -4.2Subproblem 2
x + 5 = -0.8 Simplifying x + 5 = -0.8 Reorder the terms: 5 + x = -0.8 Solving 5 + x = -0.8 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 = -0.8 + -5 Combine like terms: 5 + -5 = 0 0 + x = -0.8 + -5 x = -0.8 + -5 Combine like terms: -0.8 + -5 = -5.8 x = -5.8 Simplifying x = -5.8Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.2, -5.8}
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