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Simplifying x2 + 15x = 222 Reorder the terms: 15x + x2 = 222 Solving 15x + x2 = 222 Solving for variable 'x'. Reorder the terms: -222 + 15x + x2 = 222 + -222 Combine like terms: 222 + -222 = 0 -222 + 15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '222' to each side of the equation. -222 + 15x + 222 + x2 = 0 + 222 Reorder the terms: -222 + 222 + 15x + x2 = 0 + 222 Combine like terms: -222 + 222 = 0 0 + 15x + x2 = 0 + 222 15x + x2 = 0 + 222 Combine like terms: 0 + 222 = 222 15x + x2 = 222 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = 222 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 222 + 56.25 Combine like terms: 222 + 56.25 = 278.25 56.25 + 15x + x2 = 278.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 278.25 Calculate the square root of the right side: 16.680827318 Break this problem into two subproblems by setting (x + 7.5) equal to 16.680827318 and -16.680827318.Subproblem 1
x + 7.5 = 16.680827318 Simplifying x + 7.5 = 16.680827318 Reorder the terms: 7.5 + x = 16.680827318 Solving 7.5 + x = 16.680827318 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 16.680827318 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 16.680827318 + -7.5 x = 16.680827318 + -7.5 Combine like terms: 16.680827318 + -7.5 = 9.180827318 x = 9.180827318 Simplifying x = 9.180827318Subproblem 2
x + 7.5 = -16.680827318 Simplifying x + 7.5 = -16.680827318 Reorder the terms: 7.5 + x = -16.680827318 Solving 7.5 + x = -16.680827318 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -16.680827318 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -16.680827318 + -7.5 x = -16.680827318 + -7.5 Combine like terms: -16.680827318 + -7.5 = -24.180827318 x = -24.180827318 Simplifying x = -24.180827318Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.180827318, -24.180827318}
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