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Simplifying x2 + -0.03x + -59.521 = 0 Reorder the terms: -59.521 + -0.03x + x2 = 0 Solving -59.521 + -0.03x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '59.521' to each side of the equation. -59.521 + -0.03x + 59.521 + x2 = 0 + 59.521 Reorder the terms: -59.521 + 59.521 + -0.03x + x2 = 0 + 59.521 Combine like terms: -59.521 + 59.521 = 0.000 0.000 + -0.03x + x2 = 0 + 59.521 -0.03x + x2 = 0 + 59.521 Combine like terms: 0 + 59.521 = 59.521 -0.03x + x2 = 59.521 The x term is -0.03x. Take half its coefficient (-0.015). Square it (0.000225) and add it to both sides. Add '0.000225' to each side of the equation. -0.03x + 0.000225 + x2 = 59.521 + 0.000225 Reorder the terms: 0.000225 + -0.03x + x2 = 59.521 + 0.000225 Combine like terms: 59.521 + 0.000225 = 59.521225 0.000225 + -0.03x + x2 = 59.521225 Factor a perfect square on the left side: (x + -0.015)(x + -0.015) = 59.521225 Calculate the square root of the right side: 7.715 Break this problem into two subproblems by setting (x + -0.015) equal to 7.715 and -7.715.Subproblem 1
x + -0.015 = 7.715 Simplifying x + -0.015 = 7.715 Reorder the terms: -0.015 + x = 7.715 Solving -0.015 + x = 7.715 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.015' to each side of the equation. -0.015 + 0.015 + x = 7.715 + 0.015 Combine like terms: -0.015 + 0.015 = 0.000 0.000 + x = 7.715 + 0.015 x = 7.715 + 0.015 Combine like terms: 7.715 + 0.015 = 7.73 x = 7.73 Simplifying x = 7.73Subproblem 2
x + -0.015 = -7.715 Simplifying x + -0.015 = -7.715 Reorder the terms: -0.015 + x = -7.715 Solving -0.015 + x = -7.715 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.015' to each side of the equation. -0.015 + 0.015 + x = -7.715 + 0.015 Combine like terms: -0.015 + 0.015 = 0.000 0.000 + x = -7.715 + 0.015 x = -7.715 + 0.015 Combine like terms: -7.715 + 0.015 = -7.7 x = -7.7 Simplifying x = -7.7Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.73, -7.7}
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