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Simplifying 5x2 + 42x + -18 = 180 Reorder the terms: -18 + 42x + 5x2 = 180 Solving -18 + 42x + 5x2 = 180 Solving for variable 'x'. Reorder the terms: -18 + -180 + 42x + 5x2 = 180 + -180 Combine like terms: -18 + -180 = -198 -198 + 42x + 5x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -198 + 42x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -39.6 + 8.4x + x2 = 0 Move the constant term to the right: Add '39.6' to each side of the equation. -39.6 + 8.4x + 39.6 + x2 = 0 + 39.6 Reorder the terms: -39.6 + 39.6 + 8.4x + x2 = 0 + 39.6 Combine like terms: -39.6 + 39.6 = 0.0 0.0 + 8.4x + x2 = 0 + 39.6 8.4x + x2 = 0 + 39.6 Combine like terms: 0 + 39.6 = 39.6 8.4x + x2 = 39.6 The x term is 8.4x. Take half its coefficient (4.2). Square it (17.64) and add it to both sides. Add '17.64' to each side of the equation. 8.4x + 17.64 + x2 = 39.6 + 17.64 Reorder the terms: 17.64 + 8.4x + x2 = 39.6 + 17.64 Combine like terms: 39.6 + 17.64 = 57.24 17.64 + 8.4x + x2 = 57.24 Factor a perfect square on the left side: (x + 4.2)(x + 4.2) = 57.24 Calculate the square root of the right side: 7.565712128 Break this problem into two subproblems by setting (x + 4.2) equal to 7.565712128 and -7.565712128.Subproblem 1
x + 4.2 = 7.565712128 Simplifying x + 4.2 = 7.565712128 Reorder the terms: 4.2 + x = 7.565712128 Solving 4.2 + x = 7.565712128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.2' to each side of the equation. 4.2 + -4.2 + x = 7.565712128 + -4.2 Combine like terms: 4.2 + -4.2 = 0.0 0.0 + x = 7.565712128 + -4.2 x = 7.565712128 + -4.2 Combine like terms: 7.565712128 + -4.2 = 3.365712128 x = 3.365712128 Simplifying x = 3.365712128Subproblem 2
x + 4.2 = -7.565712128 Simplifying x + 4.2 = -7.565712128 Reorder the terms: 4.2 + x = -7.565712128 Solving 4.2 + x = -7.565712128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.2' to each side of the equation. 4.2 + -4.2 + x = -7.565712128 + -4.2 Combine like terms: 4.2 + -4.2 = 0.0 0.0 + x = -7.565712128 + -4.2 x = -7.565712128 + -4.2 Combine like terms: -7.565712128 + -4.2 = -11.765712128 x = -11.765712128 Simplifying x = -11.765712128Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.365712128, -11.765712128}
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