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Simplifying 4x2 + -25x + 33 = 0 Reorder the terms: 33 + -25x + 4x2 = 0 Solving 33 + -25x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 8.25 + -6.25x + x2 = 0 Move the constant term to the right: Add '-8.25' to each side of the equation. 8.25 + -6.25x + -8.25 + x2 = 0 + -8.25 Reorder the terms: 8.25 + -8.25 + -6.25x + x2 = 0 + -8.25 Combine like terms: 8.25 + -8.25 = 0.00 0.00 + -6.25x + x2 = 0 + -8.25 -6.25x + x2 = 0 + -8.25 Combine like terms: 0 + -8.25 = -8.25 -6.25x + x2 = -8.25 The x term is -6.25x. Take half its coefficient (-3.125). Square it (9.765625) and add it to both sides. Add '9.765625' to each side of the equation. -6.25x + 9.765625 + x2 = -8.25 + 9.765625 Reorder the terms: 9.765625 + -6.25x + x2 = -8.25 + 9.765625 Combine like terms: -8.25 + 9.765625 = 1.515625 9.765625 + -6.25x + x2 = 1.515625 Factor a perfect square on the left side: (x + -3.125)(x + -3.125) = 1.515625 Calculate the square root of the right side: 1.231107225 Break this problem into two subproblems by setting (x + -3.125) equal to 1.231107225 and -1.231107225.Subproblem 1
x + -3.125 = 1.231107225 Simplifying x + -3.125 = 1.231107225 Reorder the terms: -3.125 + x = 1.231107225 Solving -3.125 + x = 1.231107225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = 1.231107225 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = 1.231107225 + 3.125 x = 1.231107225 + 3.125 Combine like terms: 1.231107225 + 3.125 = 4.356107225 x = 4.356107225 Simplifying x = 4.356107225Subproblem 2
x + -3.125 = -1.231107225 Simplifying x + -3.125 = -1.231107225 Reorder the terms: -3.125 + x = -1.231107225 Solving -3.125 + x = -1.231107225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = -1.231107225 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = -1.231107225 + 3.125 x = -1.231107225 + 3.125 Combine like terms: -1.231107225 + 3.125 = 1.893892775 x = 1.893892775 Simplifying x = 1.893892775Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.356107225, 1.893892775}
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