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Simplifying 0.0064x2 + -0.64x + 12 = 0 Reorder the terms: 12 + -0.64x + 0.0064x2 = 0 Solving 12 + -0.64x + 0.0064x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.0064 the coefficient of the squared term: Divide each side by '0.0064'. 1875 + -100x + x2 = 0 Move the constant term to the right: Add '-1875' to each side of the equation. 1875 + -100x + -1875 + x2 = 0 + -1875 Reorder the terms: 1875 + -1875 + -100x + x2 = 0 + -1875 Combine like terms: 1875 + -1875 = 0 0 + -100x + x2 = 0 + -1875 -100x + x2 = 0 + -1875 Combine like terms: 0 + -1875 = -1875 -100x + x2 = -1875 The x term is -100x. Take half its coefficient (-50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. -100x + 2500 + x2 = -1875 + 2500 Reorder the terms: 2500 + -100x + x2 = -1875 + 2500 Combine like terms: -1875 + 2500 = 625 2500 + -100x + x2 = 625 Factor a perfect square on the left side: (x + -50)(x + -50) = 625 Calculate the square root of the right side: 25 Break this problem into two subproblems by setting (x + -50) equal to 25 and -25.Subproblem 1
x + -50 = 25 Simplifying x + -50 = 25 Reorder the terms: -50 + x = 25 Solving -50 + x = 25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = 25 + 50 Combine like terms: -50 + 50 = 0 0 + x = 25 + 50 x = 25 + 50 Combine like terms: 25 + 50 = 75 x = 75 Simplifying x = 75Subproblem 2
x + -50 = -25 Simplifying x + -50 = -25 Reorder the terms: -50 + x = -25 Solving -50 + x = -25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = -25 + 50 Combine like terms: -50 + 50 = 0 0 + x = -25 + 50 x = -25 + 50 Combine like terms: -25 + 50 = 25 x = 25 Simplifying x = 25Solution
The solution to the problem is based on the solutions from the subproblems. x = {75, 25}
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