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Simplifying 4x2 + 25x + 25 = 4480 Reorder the terms: 25 + 25x + 4x2 = 4480 Solving 25 + 25x + 4x2 = 4480 Solving for variable 'x'. Reorder the terms: 25 + -4480 + 25x + 4x2 = 4480 + -4480 Combine like terms: 25 + -4480 = -4455 -4455 + 25x + 4x2 = 4480 + -4480 Combine like terms: 4480 + -4480 = 0 -4455 + 25x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1113.75 + 6.25x + x2 = 0 Move the constant term to the right: Add '1113.75' to each side of the equation. -1113.75 + 6.25x + 1113.75 + x2 = 0 + 1113.75 Reorder the terms: -1113.75 + 1113.75 + 6.25x + x2 = 0 + 1113.75 Combine like terms: -1113.75 + 1113.75 = 0.00 0.00 + 6.25x + x2 = 0 + 1113.75 6.25x + x2 = 0 + 1113.75 Combine like terms: 0 + 1113.75 = 1113.75 6.25x + x2 = 1113.75 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 = 1113.75 + 9.765625 Reorder the terms: 9.765625 + 6.25x + x2 = 1113.75 + 9.765625 Combine like terms: 1113.75 + 9.765625 = 1123.515625 9.765625 + 6.25x + x2 = 1123.515625 Factor a perfect square on the left side: (x + 3.125)(x + 3.125) = 1123.515625 Calculate the square root of the right side: 33.518884603 Break this problem into two subproblems by setting (x + 3.125) equal to 33.518884603 and -33.518884603.Subproblem 1
x + 3.125 = 33.518884603 Simplifying x + 3.125 = 33.518884603 Reorder the terms: 3.125 + x = 33.518884603 Solving 3.125 + x = 33.518884603 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 = 33.518884603 + -3.125 Combine like terms: 3.125 + -3.125 = 0.000 0.000 + x = 33.518884603 + -3.125 x = 33.518884603 + -3.125 Combine like terms: 33.518884603 + -3.125 = 30.393884603 x = 30.393884603 Simplifying x = 30.393884603Subproblem 2
x + 3.125 = -33.518884603 Simplifying x + 3.125 = -33.518884603 Reorder the terms: 3.125 + x = -33.518884603 Solving 3.125 + x = -33.518884603 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 = -33.518884603 + -3.125 Combine like terms: 3.125 + -3.125 = 0.000 0.000 + x = -33.518884603 + -3.125 x = -33.518884603 + -3.125 Combine like terms: -33.518884603 + -3.125 = -36.643884603 x = -36.643884603 Simplifying x = -36.643884603Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.393884603, -36.643884603}
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