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Simplifying 8x2 + 20x = 53 Reorder the terms: 20x + 8x2 = 53 Solving 20x + 8x2 = 53 Solving for variable 'x'. Reorder the terms: -53 + 20x + 8x2 = 53 + -53 Combine like terms: 53 + -53 = 0 -53 + 20x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -6.625 + 2.5x + x2 = 0 Move the constant term to the right: Add '6.625' to each side of the equation. -6.625 + 2.5x + 6.625 + x2 = 0 + 6.625 Reorder the terms: -6.625 + 6.625 + 2.5x + x2 = 0 + 6.625 Combine like terms: -6.625 + 6.625 = 0.000 0.000 + 2.5x + x2 = 0 + 6.625 2.5x + x2 = 0 + 6.625 Combine like terms: 0 + 6.625 = 6.625 2.5x + x2 = 6.625 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 6.625 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 6.625 + 1.5625 Combine like terms: 6.625 + 1.5625 = 8.1875 1.5625 + 2.5x + x2 = 8.1875 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 8.1875 Calculate the square root of the right side: 2.861380786 Break this problem into two subproblems by setting (x + 1.25) equal to 2.861380786 and -2.861380786.Subproblem 1
x + 1.25 = 2.861380786 Simplifying x + 1.25 = 2.861380786 Reorder the terms: 1.25 + x = 2.861380786 Solving 1.25 + x = 2.861380786 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 2.861380786 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 2.861380786 + -1.25 x = 2.861380786 + -1.25 Combine like terms: 2.861380786 + -1.25 = 1.611380786 x = 1.611380786 Simplifying x = 1.611380786Subproblem 2
x + 1.25 = -2.861380786 Simplifying x + 1.25 = -2.861380786 Reorder the terms: 1.25 + x = -2.861380786 Solving 1.25 + x = -2.861380786 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -2.861380786 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -2.861380786 + -1.25 x = -2.861380786 + -1.25 Combine like terms: -2.861380786 + -1.25 = -4.111380786 x = -4.111380786 Simplifying x = -4.111380786Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.611380786, -4.111380786}
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