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Simplifying 0.25x2 + -10x + 64 = 0 Reorder the terms: 64 + -10x + 0.25x2 = 0 Solving 64 + -10x + 0.25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. 256 + -40x + x2 = 0 Move the constant term to the right: Add '-256' to each side of the equation. 256 + -40x + -256 + x2 = 0 + -256 Reorder the terms: 256 + -256 + -40x + x2 = 0 + -256 Combine like terms: 256 + -256 = 0 0 + -40x + x2 = 0 + -256 -40x + x2 = 0 + -256 Combine like terms: 0 + -256 = -256 -40x + x2 = -256 The x term is -40x. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40x + 400 + x2 = -256 + 400 Reorder the terms: 400 + -40x + x2 = -256 + 400 Combine like terms: -256 + 400 = 144 400 + -40x + x2 = 144 Factor a perfect square on the left side: (x + -20)(x + -20) = 144 Calculate the square root of the right side: 12 Break this problem into two subproblems by setting (x + -20) equal to 12 and -12.Subproblem 1
x + -20 = 12 Simplifying x + -20 = 12 Reorder the terms: -20 + x = 12 Solving -20 + x = 12 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 12 + 20 Combine like terms: -20 + 20 = 0 0 + x = 12 + 20 x = 12 + 20 Combine like terms: 12 + 20 = 32 x = 32 Simplifying x = 32Subproblem 2
x + -20 = -12 Simplifying x + -20 = -12 Reorder the terms: -20 + x = -12 Solving -20 + x = -12 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -12 + 20 Combine like terms: -20 + 20 = 0 0 + x = -12 + 20 x = -12 + 20 Combine like terms: -12 + 20 = 8 x = 8 Simplifying x = 8Solution
The solution to the problem is based on the solutions from the subproblems. x = {32, 8}
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