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Simplifying 12x + 200 = x2 Reorder the terms: 200 + 12x = x2 Solving 200 + 12x = x2 Solving for variable 'x'. Combine like terms: x2 + -1x2 = 0 200 + 12x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -200 + -12x + x2 = 0 Move the constant term to the right: Add '200' to each side of the equation. -200 + -12x + 200 + x2 = 0 + 200 Reorder the terms: -200 + 200 + -12x + x2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + -12x + x2 = 0 + 200 -12x + x2 = 0 + 200 Combine like terms: 0 + 200 = 200 -12x + x2 = 200 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 200 + 36 Reorder the terms: 36 + -12x + x2 = 200 + 36 Combine like terms: 200 + 36 = 236 36 + -12x + x2 = 236 Factor a perfect square on the left side: (x + -6)(x + -6) = 236 Calculate the square root of the right side: 15.362291496 Break this problem into two subproblems by setting (x + -6) equal to 15.362291496 and -15.362291496.Subproblem 1
x + -6 = 15.362291496 Simplifying x + -6 = 15.362291496 Reorder the terms: -6 + x = 15.362291496 Solving -6 + x = 15.362291496 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 15.362291496 + 6 Combine like terms: -6 + 6 = 0 0 + x = 15.362291496 + 6 x = 15.362291496 + 6 Combine like terms: 15.362291496 + 6 = 21.362291496 x = 21.362291496 Simplifying x = 21.362291496Subproblem 2
x + -6 = -15.362291496 Simplifying x + -6 = -15.362291496 Reorder the terms: -6 + x = -15.362291496 Solving -6 + x = -15.362291496 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -15.362291496 + 6 Combine like terms: -6 + 6 = 0 0 + x = -15.362291496 + 6 x = -15.362291496 + 6 Combine like terms: -15.362291496 + 6 = -9.362291496 x = -9.362291496 Simplifying x = -9.362291496Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.362291496, -9.362291496}
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