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Simplifying 25x2 + -280x + -51 = 0 Reorder the terms: -51 + -280x + 25x2 = 0 Solving -51 + -280x + 25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -2.04 + -11.2x + x2 = 0 Move the constant term to the right: Add '2.04' to each side of the equation. -2.04 + -11.2x + 2.04 + x2 = 0 + 2.04 Reorder the terms: -2.04 + 2.04 + -11.2x + x2 = 0 + 2.04 Combine like terms: -2.04 + 2.04 = 0.00 0.00 + -11.2x + x2 = 0 + 2.04 -11.2x + x2 = 0 + 2.04 Combine like terms: 0 + 2.04 = 2.04 -11.2x + x2 = 2.04 The x term is -11.2x. Take half its coefficient (-5.6). Square it (31.36) and add it to both sides. Add '31.36' to each side of the equation. -11.2x + 31.36 + x2 = 2.04 + 31.36 Reorder the terms: 31.36 + -11.2x + x2 = 2.04 + 31.36 Combine like terms: 2.04 + 31.36 = 33.4 31.36 + -11.2x + x2 = 33.4 Factor a perfect square on the left side: (x + -5.6)(x + -5.6) = 33.4 Calculate the square root of the right side: 5.779273311 Break this problem into two subproblems by setting (x + -5.6) equal to 5.779273311 and -5.779273311.Subproblem 1
x + -5.6 = 5.779273311 Simplifying x + -5.6 = 5.779273311 Reorder the terms: -5.6 + x = 5.779273311 Solving -5.6 + x = 5.779273311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.6' to each side of the equation. -5.6 + 5.6 + x = 5.779273311 + 5.6 Combine like terms: -5.6 + 5.6 = 0.0 0.0 + x = 5.779273311 + 5.6 x = 5.779273311 + 5.6 Combine like terms: 5.779273311 + 5.6 = 11.379273311 x = 11.379273311 Simplifying x = 11.379273311Subproblem 2
x + -5.6 = -5.779273311 Simplifying x + -5.6 = -5.779273311 Reorder the terms: -5.6 + x = -5.779273311 Solving -5.6 + x = -5.779273311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.6' to each side of the equation. -5.6 + 5.6 + x = -5.779273311 + 5.6 Combine like terms: -5.6 + 5.6 = 0.0 0.0 + x = -5.779273311 + 5.6 x = -5.779273311 + 5.6 Combine like terms: -5.779273311 + 5.6 = -0.179273311 x = -0.179273311 Simplifying x = -0.179273311Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.379273311, -0.179273311}
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