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Simplifying 50x + -6.25x * x = 99 Multiply x * x 50x + -6.25x2 = 99 Solving 50x + -6.25x2 = 99 Solving for variable 'x'. Reorder the terms: -99 + 50x + -6.25x2 = 99 + -99 Combine like terms: 99 + -99 = 0 -99 + 50x + -6.25x2 = 0 Begin completing the square. Divide all terms by -6.25 the coefficient of the squared term: Divide each side by '-6.25'. 15.84 + -8x + x2 = 0 Move the constant term to the right: Add '-15.84' to each side of the equation. 15.84 + -8x + -15.84 + x2 = 0 + -15.84 Reorder the terms: 15.84 + -15.84 + -8x + x2 = 0 + -15.84 Combine like terms: 15.84 + -15.84 = 0.00 0.00 + -8x + x2 = 0 + -15.84 -8x + x2 = 0 + -15.84 Combine like terms: 0 + -15.84 = -15.84 -8x + x2 = -15.84 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -15.84 + 16 Reorder the terms: 16 + -8x + x2 = -15.84 + 16 Combine like terms: -15.84 + 16 = 0.16 16 + -8x + x2 = 0.16 Factor a perfect square on the left side: (x + -4)(x + -4) = 0.16 Calculate the square root of the right side: 0.4 Break this problem into two subproblems by setting (x + -4) equal to 0.4 and -0.4.Subproblem 1
x + -4 = 0.4 Simplifying x + -4 = 0.4 Reorder the terms: -4 + x = 0.4 Solving -4 + x = 0.4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 0.4 + 4 Combine like terms: -4 + 4 = 0 0 + x = 0.4 + 4 x = 0.4 + 4 Combine like terms: 0.4 + 4 = 4.4 x = 4.4 Simplifying x = 4.4Subproblem 2
x + -4 = -0.4 Simplifying x + -4 = -0.4 Reorder the terms: -4 + x = -0.4 Solving -4 + x = -0.4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -0.4 + 4 Combine like terms: -4 + 4 = 0 0 + x = -0.4 + 4 x = -0.4 + 4 Combine like terms: -0.4 + 4 = 3.6 x = 3.6 Simplifying x = 3.6Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.4, 3.6}
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