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Simplifying 8x2 + 20x = 57 Reorder the terms: 20x + 8x2 = 57 Solving 20x + 8x2 = 57 Solving for variable 'x'. Reorder the terms: -57 + 20x + 8x2 = 57 + -57 Combine like terms: 57 + -57 = 0 -57 + 20x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -7.125 + 2.5x + x2 = 0 Move the constant term to the right: Add '7.125' to each side of the equation. -7.125 + 2.5x + 7.125 + x2 = 0 + 7.125 Reorder the terms: -7.125 + 7.125 + 2.5x + x2 = 0 + 7.125 Combine like terms: -7.125 + 7.125 = 0.000 0.000 + 2.5x + x2 = 0 + 7.125 2.5x + x2 = 0 + 7.125 Combine like terms: 0 + 7.125 = 7.125 2.5x + x2 = 7.125 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 = 7.125 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 7.125 + 1.5625 Combine like terms: 7.125 + 1.5625 = 8.6875 1.5625 + 2.5x + x2 = 8.6875 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 8.6875 Calculate the square root of the right side: 2.947456531 Break this problem into two subproblems by setting (x + 1.25) equal to 2.947456531 and -2.947456531.Subproblem 1
x + 1.25 = 2.947456531 Simplifying x + 1.25 = 2.947456531 Reorder the terms: 1.25 + x = 2.947456531 Solving 1.25 + x = 2.947456531 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 = 2.947456531 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 2.947456531 + -1.25 x = 2.947456531 + -1.25 Combine like terms: 2.947456531 + -1.25 = 1.697456531 x = 1.697456531 Simplifying x = 1.697456531Subproblem 2
x + 1.25 = -2.947456531 Simplifying x + 1.25 = -2.947456531 Reorder the terms: 1.25 + x = -2.947456531 Solving 1.25 + x = -2.947456531 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 = -2.947456531 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -2.947456531 + -1.25 x = -2.947456531 + -1.25 Combine like terms: -2.947456531 + -1.25 = -4.197456531 x = -4.197456531 Simplifying x = -4.197456531Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.697456531, -4.197456531}
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