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Simplifying 4x2 + -121x + 225 = 0 Reorder the terms: 225 + -121x + 4x2 = 0 Solving 225 + -121x + 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'. 56.25 + -30.25x + x2 = 0 Move the constant term to the right: Add '-56.25' to each side of the equation. 56.25 + -30.25x + -56.25 + x2 = 0 + -56.25 Reorder the terms: 56.25 + -56.25 + -30.25x + x2 = 0 + -56.25 Combine like terms: 56.25 + -56.25 = 0.00 0.00 + -30.25x + x2 = 0 + -56.25 -30.25x + x2 = 0 + -56.25 Combine like terms: 0 + -56.25 = -56.25 -30.25x + x2 = -56.25 The x term is -30.25x. Take half its coefficient (-15.125). Square it (228.765625) and add it to both sides. Add '228.765625' to each side of the equation. -30.25x + 228.765625 + x2 = -56.25 + 228.765625 Reorder the terms: 228.765625 + -30.25x + x2 = -56.25 + 228.765625 Combine like terms: -56.25 + 228.765625 = 172.515625 228.765625 + -30.25x + x2 = 172.515625 Factor a perfect square on the left side: (x + -15.125)(x + -15.125) = 172.515625 Calculate the square root of the right side: 13.134520357 Break this problem into two subproblems by setting (x + -15.125) equal to 13.134520357 and -13.134520357.Subproblem 1
x + -15.125 = 13.134520357 Simplifying x + -15.125 = 13.134520357 Reorder the terms: -15.125 + x = 13.134520357 Solving -15.125 + x = 13.134520357 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.125' to each side of the equation. -15.125 + 15.125 + x = 13.134520357 + 15.125 Combine like terms: -15.125 + 15.125 = 0.000 0.000 + x = 13.134520357 + 15.125 x = 13.134520357 + 15.125 Combine like terms: 13.134520357 + 15.125 = 28.259520357 x = 28.259520357 Simplifying x = 28.259520357Subproblem 2
x + -15.125 = -13.134520357 Simplifying x + -15.125 = -13.134520357 Reorder the terms: -15.125 + x = -13.134520357 Solving -15.125 + x = -13.134520357 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.125' to each side of the equation. -15.125 + 15.125 + x = -13.134520357 + 15.125 Combine like terms: -15.125 + 15.125 = 0.000 0.000 + x = -13.134520357 + 15.125 x = -13.134520357 + 15.125 Combine like terms: -13.134520357 + 15.125 = 1.990479643 x = 1.990479643 Simplifying x = 1.990479643Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.259520357, 1.990479643}
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