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Simplifying 8x + 140 = x2 Reorder the terms: 140 + 8x = x2 Solving 140 + 8x = x2 Solving for variable 'x'. Combine like terms: x2 + -1x2 = 0 140 + 8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -140 + -8x + x2 = 0 Move the constant term to the right: Add '140' to each side of the equation. -140 + -8x + 140 + x2 = 0 + 140 Reorder the terms: -140 + 140 + -8x + x2 = 0 + 140 Combine like terms: -140 + 140 = 0 0 + -8x + x2 = 0 + 140 -8x + x2 = 0 + 140 Combine like terms: 0 + 140 = 140 -8x + x2 = 140 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 140 + 16 Reorder the terms: 16 + -8x + x2 = 140 + 16 Combine like terms: 140 + 16 = 156 16 + -8x + x2 = 156 Factor a perfect square on the left side: (x + -4)(x + -4) = 156 Calculate the square root of the right side: 12.489995997 Break this problem into two subproblems by setting (x + -4) equal to 12.489995997 and -12.489995997.Subproblem 1
x + -4 = 12.489995997 Simplifying x + -4 = 12.489995997 Reorder the terms: -4 + x = 12.489995997 Solving -4 + x = 12.489995997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 12.489995997 + 4 Combine like terms: -4 + 4 = 0 0 + x = 12.489995997 + 4 x = 12.489995997 + 4 Combine like terms: 12.489995997 + 4 = 16.489995997 x = 16.489995997 Simplifying x = 16.489995997Subproblem 2
x + -4 = -12.489995997 Simplifying x + -4 = -12.489995997 Reorder the terms: -4 + x = -12.489995997 Solving -4 + x = -12.489995997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -12.489995997 + 4 Combine like terms: -4 + 4 = 0 0 + x = -12.489995997 + 4 x = -12.489995997 + 4 Combine like terms: -12.489995997 + 4 = -8.489995997 x = -8.489995997 Simplifying x = -8.489995997Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.489995997, -8.489995997}
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