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Simplifying 5x2 + -36x + 60 = 0 Reorder the terms: 60 + -36x + 5x2 = 0 Solving 60 + -36x + 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'. 12 + -7.2x + x2 = 0 Move the constant term to the right: Add '-12' to each side of the equation. 12 + -7.2x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + -7.2x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -7.2x + x2 = 0 + -12 -7.2x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 -7.2x + x2 = -12 The x term is -7.2x. Take half its coefficient (-3.6). Square it (12.96) and add it to both sides. Add '12.96' to each side of the equation. -7.2x + 12.96 + x2 = -12 + 12.96 Reorder the terms: 12.96 + -7.2x + x2 = -12 + 12.96 Combine like terms: -12 + 12.96 = 0.96 12.96 + -7.2x + x2 = 0.96 Factor a perfect square on the left side: (x + -3.6)(x + -3.6) = 0.96 Calculate the square root of the right side: 0.979795897 Break this problem into two subproblems by setting (x + -3.6) equal to 0.979795897 and -0.979795897.Subproblem 1
x + -3.6 = 0.979795897 Simplifying x + -3.6 = 0.979795897 Reorder the terms: -3.6 + x = 0.979795897 Solving -3.6 + x = 0.979795897 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.6' to each side of the equation. -3.6 + 3.6 + x = 0.979795897 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + x = 0.979795897 + 3.6 x = 0.979795897 + 3.6 Combine like terms: 0.979795897 + 3.6 = 4.579795897 x = 4.579795897 Simplifying x = 4.579795897Subproblem 2
x + -3.6 = -0.979795897 Simplifying x + -3.6 = -0.979795897 Reorder the terms: -3.6 + x = -0.979795897 Solving -3.6 + x = -0.979795897 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.6' to each side of the equation. -3.6 + 3.6 + x = -0.979795897 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + x = -0.979795897 + 3.6 x = -0.979795897 + 3.6 Combine like terms: -0.979795897 + 3.6 = 2.620204103 x = 2.620204103 Simplifying x = 2.620204103Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.579795897, 2.620204103}
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