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Simplifying x2 + 1.68x = 0.3 Reorder the terms: 1.68x + x2 = 0.3 Solving 1.68x + x2 = 0.3 Solving for variable 'x'. Reorder the terms: -0.3 + 1.68x + x2 = 0.3 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 -0.3 + 1.68x + x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '0.3' to each side of the equation. -0.3 + 1.68x + 0.3 + x2 = 0.0 + 0.3 Reorder the terms: -0.3 + 0.3 + 1.68x + x2 = 0.0 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + 1.68x + x2 = 0.0 + 0.3 1.68x + x2 = 0.0 + 0.3 Combine like terms: 0.0 + 0.3 = 0.3 1.68x + x2 = 0.3 The x term is 1.68x. Take half its coefficient (0.84). Square it (0.7056) and add it to both sides. Add '0.7056' to each side of the equation. 1.68x + 0.7056 + x2 = 0.3 + 0.7056 Reorder the terms: 0.7056 + 1.68x + x2 = 0.3 + 0.7056 Combine like terms: 0.3 + 0.7056 = 1.0056 0.7056 + 1.68x + x2 = 1.0056 Factor a perfect square on the left side: (x + 0.84)(x + 0.84) = 1.0056 Calculate the square root of the right side: 1.002796091 Break this problem into two subproblems by setting (x + 0.84) equal to 1.002796091 and -1.002796091.Subproblem 1
x + 0.84 = 1.002796091 Simplifying x + 0.84 = 1.002796091 Reorder the terms: 0.84 + x = 1.002796091 Solving 0.84 + x = 1.002796091 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.84' to each side of the equation. 0.84 + -0.84 + x = 1.002796091 + -0.84 Combine like terms: 0.84 + -0.84 = 0.00 0.00 + x = 1.002796091 + -0.84 x = 1.002796091 + -0.84 Combine like terms: 1.002796091 + -0.84 = 0.162796091 x = 0.162796091 Simplifying x = 0.162796091Subproblem 2
x + 0.84 = -1.002796091 Simplifying x + 0.84 = -1.002796091 Reorder the terms: 0.84 + x = -1.002796091 Solving 0.84 + x = -1.002796091 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.84' to each side of the equation. 0.84 + -0.84 + x = -1.002796091 + -0.84 Combine like terms: 0.84 + -0.84 = 0.00 0.00 + x = -1.002796091 + -0.84 x = -1.002796091 + -0.84 Combine like terms: -1.002796091 + -0.84 = -1.842796091 x = -1.842796091 Simplifying x = -1.842796091Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.162796091, -1.842796091}
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