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Simplifying X2 + 14X + -476.188 = 0 Reorder the terms: -476.188 + 14X + X2 = 0 Solving -476.188 + 14X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '476.188' to each side of the equation. -476.188 + 14X + 476.188 + X2 = 0 + 476.188 Reorder the terms: -476.188 + 476.188 + 14X + X2 = 0 + 476.188 Combine like terms: -476.188 + 476.188 = 0.000 0.000 + 14X + X2 = 0 + 476.188 14X + X2 = 0 + 476.188 Combine like terms: 0 + 476.188 = 476.188 14X + X2 = 476.188 The X term is 14X. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14X + 49 + X2 = 476.188 + 49 Reorder the terms: 49 + 14X + X2 = 476.188 + 49 Combine like terms: 476.188 + 49 = 525.188 49 + 14X + X2 = 525.188 Factor a perfect square on the left side: (X + 7)(X + 7) = 525.188 Calculate the square root of the right side: 22.916980604 Break this problem into two subproblems by setting (X + 7) equal to 22.916980604 and -22.916980604.Subproblem 1
X + 7 = 22.916980604 Simplifying X + 7 = 22.916980604 Reorder the terms: 7 + X = 22.916980604 Solving 7 + X = 22.916980604 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + X = 22.916980604 + -7 Combine like terms: 7 + -7 = 0 0 + X = 22.916980604 + -7 X = 22.916980604 + -7 Combine like terms: 22.916980604 + -7 = 15.916980604 X = 15.916980604 Simplifying X = 15.916980604Subproblem 2
X + 7 = -22.916980604 Simplifying X + 7 = -22.916980604 Reorder the terms: 7 + X = -22.916980604 Solving 7 + X = -22.916980604 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + X = -22.916980604 + -7 Combine like terms: 7 + -7 = 0 0 + X = -22.916980604 + -7 X = -22.916980604 + -7 Combine like terms: -22.916980604 + -7 = -29.916980604 X = -29.916980604 Simplifying X = -29.916980604Solution
The solution to the problem is based on the solutions from the subproblems. X = {15.916980604, -29.916980604}
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