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Simplifying x + 7 + -5x2 + 70x + 245 = 0 Reorder the terms: 7 + 245 + x + 70x + -5x2 = 0 Combine like terms: 7 + 245 = 252 252 + x + 70x + -5x2 = 0 Combine like terms: x + 70x = 71x 252 + 71x + -5x2 = 0 Solving 252 + 71x + -5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -50.4 + -14.2x + x2 = 0 Move the constant term to the right: Add '50.4' to each side of the equation. -50.4 + -14.2x + 50.4 + x2 = 0 + 50.4 Reorder the terms: -50.4 + 50.4 + -14.2x + x2 = 0 + 50.4 Combine like terms: -50.4 + 50.4 = 0.0 0.0 + -14.2x + x2 = 0 + 50.4 -14.2x + x2 = 0 + 50.4 Combine like terms: 0 + 50.4 = 50.4 -14.2x + x2 = 50.4 The x term is -14.2x. Take half its coefficient (-7.1). Square it (50.41) and add it to both sides. Add '50.41' to each side of the equation. -14.2x + 50.41 + x2 = 50.4 + 50.41 Reorder the terms: 50.41 + -14.2x + x2 = 50.4 + 50.41 Combine like terms: 50.4 + 50.41 = 100.81 50.41 + -14.2x + x2 = 100.81 Factor a perfect square on the left side: (x + -7.1)(x + -7.1) = 100.81 Calculate the square root of the right side: 10.040418318 Break this problem into two subproblems by setting (x + -7.1) equal to 10.040418318 and -10.040418318.Subproblem 1
x + -7.1 = 10.040418318 Simplifying x + -7.1 = 10.040418318 Reorder the terms: -7.1 + x = 10.040418318 Solving -7.1 + x = 10.040418318 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.1' to each side of the equation. -7.1 + 7.1 + x = 10.040418318 + 7.1 Combine like terms: -7.1 + 7.1 = 0.0 0.0 + x = 10.040418318 + 7.1 x = 10.040418318 + 7.1 Combine like terms: 10.040418318 + 7.1 = 17.140418318 x = 17.140418318 Simplifying x = 17.140418318Subproblem 2
x + -7.1 = -10.040418318 Simplifying x + -7.1 = -10.040418318 Reorder the terms: -7.1 + x = -10.040418318 Solving -7.1 + x = -10.040418318 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.1' to each side of the equation. -7.1 + 7.1 + x = -10.040418318 + 7.1 Combine like terms: -7.1 + 7.1 = 0.0 0.0 + x = -10.040418318 + 7.1 x = -10.040418318 + 7.1 Combine like terms: -10.040418318 + 7.1 = -2.940418318 x = -2.940418318 Simplifying x = -2.940418318Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.140418318, -2.940418318}
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