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Simplifying x2 + -59.8x + 644.37 = 0 Reorder the terms: 644.37 + -59.8x + x2 = 0 Solving 644.37 + -59.8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-644.37' to each side of the equation. 644.37 + -59.8x + -644.37 + x2 = 0 + -644.37 Reorder the terms: 644.37 + -644.37 + -59.8x + x2 = 0 + -644.37 Combine like terms: 644.37 + -644.37 = 0.00 0.00 + -59.8x + x2 = 0 + -644.37 -59.8x + x2 = 0 + -644.37 Combine like terms: 0 + -644.37 = -644.37 -59.8x + x2 = -644.37 The x term is -59.8x. Take half its coefficient (-29.9). Square it (894.01) and add it to both sides. Add '894.01' to each side of the equation. -59.8x + 894.01 + x2 = -644.37 + 894.01 Reorder the terms: 894.01 + -59.8x + x2 = -644.37 + 894.01 Combine like terms: -644.37 + 894.01 = 249.64 894.01 + -59.8x + x2 = 249.64 Factor a perfect square on the left side: (x + -29.9)(x + -29.9) = 249.64 Calculate the square root of the right side: 15.8 Break this problem into two subproblems by setting (x + -29.9) equal to 15.8 and -15.8.Subproblem 1
x + -29.9 = 15.8 Simplifying x + -29.9 = 15.8 Reorder the terms: -29.9 + x = 15.8 Solving -29.9 + x = 15.8 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '29.9' to each side of the equation. -29.9 + 29.9 + x = 15.8 + 29.9 Combine like terms: -29.9 + 29.9 = 0.0 0.0 + x = 15.8 + 29.9 x = 15.8 + 29.9 Combine like terms: 15.8 + 29.9 = 45.7 x = 45.7 Simplifying x = 45.7Subproblem 2
x + -29.9 = -15.8 Simplifying x + -29.9 = -15.8 Reorder the terms: -29.9 + x = -15.8 Solving -29.9 + x = -15.8 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '29.9' to each side of the equation. -29.9 + 29.9 + x = -15.8 + 29.9 Combine like terms: -29.9 + 29.9 = 0.0 0.0 + x = -15.8 + 29.9 x = -15.8 + 29.9 Combine like terms: -15.8 + 29.9 = 14.1 x = 14.1 Simplifying x = 14.1Solution
The solution to the problem is based on the solutions from the subproblems. x = {45.7, 14.1}
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