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Simplifying 7x + 2x2 = 57 Solving 7x + 2x2 = 57 Solving for variable 'x'. Reorder the terms: -57 + 7x + 2x2 = 57 + -57 Combine like terms: 57 + -57 = 0 -57 + 7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -28.5 + 3.5x + x2 = 0 Move the constant term to the right: Add '28.5' to each side of the equation. -28.5 + 3.5x + 28.5 + x2 = 0 + 28.5 Reorder the terms: -28.5 + 28.5 + 3.5x + x2 = 0 + 28.5 Combine like terms: -28.5 + 28.5 = 0.0 0.0 + 3.5x + x2 = 0 + 28.5 3.5x + x2 = 0 + 28.5 Combine like terms: 0 + 28.5 = 28.5 3.5x + x2 = 28.5 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 28.5 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 28.5 + 3.0625 Combine like terms: 28.5 + 3.0625 = 31.5625 3.0625 + 3.5x + x2 = 31.5625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 31.5625 Calculate the square root of the right side: 5.618051264 Break this problem into two subproblems by setting (x + 1.75) equal to 5.618051264 and -5.618051264.Subproblem 1
x + 1.75 = 5.618051264 Simplifying x + 1.75 = 5.618051264 Reorder the terms: 1.75 + x = 5.618051264 Solving 1.75 + x = 5.618051264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 5.618051264 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 5.618051264 + -1.75 x = 5.618051264 + -1.75 Combine like terms: 5.618051264 + -1.75 = 3.868051264 x = 3.868051264 Simplifying x = 3.868051264Subproblem 2
x + 1.75 = -5.618051264 Simplifying x + 1.75 = -5.618051264 Reorder the terms: 1.75 + x = -5.618051264 Solving 1.75 + x = -5.618051264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -5.618051264 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -5.618051264 + -1.75 x = -5.618051264 + -1.75 Combine like terms: -5.618051264 + -1.75 = -7.368051264 x = -7.368051264 Simplifying x = -7.368051264Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.868051264, -7.368051264}
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