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Simplifying 59x + x2 = 90 Solving 59x + x2 = 90 Solving for variable 'x'. Reorder the terms: -90 + 59x + x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -90 + 59x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '90' to each side of the equation. -90 + 59x + 90 + x2 = 0 + 90 Reorder the terms: -90 + 90 + 59x + x2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + 59x + x2 = 0 + 90 59x + x2 = 0 + 90 Combine like terms: 0 + 90 = 90 59x + x2 = 90 The x term is 59x. Take half its coefficient (29.5). Square it (870.25) and add it to both sides. Add '870.25' to each side of the equation. 59x + 870.25 + x2 = 90 + 870.25 Reorder the terms: 870.25 + 59x + x2 = 90 + 870.25 Combine like terms: 90 + 870.25 = 960.25 870.25 + 59x + x2 = 960.25 Factor a perfect square on the left side: (x + 29.5)(x + 29.5) = 960.25 Calculate the square root of the right side: 30.987900865 Break this problem into two subproblems by setting (x + 29.5) equal to 30.987900865 and -30.987900865.Subproblem 1
x + 29.5 = 30.987900865 Simplifying x + 29.5 = 30.987900865 Reorder the terms: 29.5 + x = 30.987900865 Solving 29.5 + x = 30.987900865 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-29.5' to each side of the equation. 29.5 + -29.5 + x = 30.987900865 + -29.5 Combine like terms: 29.5 + -29.5 = 0.0 0.0 + x = 30.987900865 + -29.5 x = 30.987900865 + -29.5 Combine like terms: 30.987900865 + -29.5 = 1.487900865 x = 1.487900865 Simplifying x = 1.487900865Subproblem 2
x + 29.5 = -30.987900865 Simplifying x + 29.5 = -30.987900865 Reorder the terms: 29.5 + x = -30.987900865 Solving 29.5 + x = -30.987900865 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-29.5' to each side of the equation. 29.5 + -29.5 + x = -30.987900865 + -29.5 Combine like terms: 29.5 + -29.5 = 0.0 0.0 + x = -30.987900865 + -29.5 x = -30.987900865 + -29.5 Combine like terms: -30.987900865 + -29.5 = -60.487900865 x = -60.487900865 Simplifying x = -60.487900865Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.487900865, -60.487900865}
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