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Simplifying 4x2 + -49x + 144 = 0 Reorder the terms: 144 + -49x + 4x2 = 0 Solving 144 + -49x + 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'. 36 + -12.25x + x2 = 0 Move the constant term to the right: Add '-36' to each side of the equation. 36 + -12.25x + -36 + x2 = 0 + -36 Reorder the terms: 36 + -36 + -12.25x + x2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -12.25x + x2 = 0 + -36 -12.25x + x2 = 0 + -36 Combine like terms: 0 + -36 = -36 -12.25x + x2 = -36 The x term is -12.25x. Take half its coefficient (-6.125). Square it (37.515625) and add it to both sides. Add '37.515625' to each side of the equation. -12.25x + 37.515625 + x2 = -36 + 37.515625 Reorder the terms: 37.515625 + -12.25x + x2 = -36 + 37.515625 Combine like terms: -36 + 37.515625 = 1.515625 37.515625 + -12.25x + x2 = 1.515625 Factor a perfect square on the left side: (x + -6.125)(x + -6.125) = 1.515625 Calculate the square root of the right side: 1.231107225 Break this problem into two subproblems by setting (x + -6.125) equal to 1.231107225 and -1.231107225.Subproblem 1
x + -6.125 = 1.231107225 Simplifying x + -6.125 = 1.231107225 Reorder the terms: -6.125 + x = 1.231107225 Solving -6.125 + x = 1.231107225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.125' to each side of the equation. -6.125 + 6.125 + x = 1.231107225 + 6.125 Combine like terms: -6.125 + 6.125 = 0.000 0.000 + x = 1.231107225 + 6.125 x = 1.231107225 + 6.125 Combine like terms: 1.231107225 + 6.125 = 7.356107225 x = 7.356107225 Simplifying x = 7.356107225Subproblem 2
x + -6.125 = -1.231107225 Simplifying x + -6.125 = -1.231107225 Reorder the terms: -6.125 + x = -1.231107225 Solving -6.125 + x = -1.231107225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.125' to each side of the equation. -6.125 + 6.125 + x = -1.231107225 + 6.125 Combine like terms: -6.125 + 6.125 = 0.000 0.000 + x = -1.231107225 + 6.125 x = -1.231107225 + 6.125 Combine like terms: -1.231107225 + 6.125 = 4.893892775 x = 4.893892775 Simplifying x = 4.893892775Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.356107225, 4.893892775}
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