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Simplifying x = -0.02x2 + 1.4x + 5.5 Reorder the terms: x = 5.5 + 1.4x + -0.02x2 Solving x = 5.5 + 1.4x + -0.02x2 Solving for variable 'x'. Reorder the terms: -5.5 + x + -1.4x + 0.02x2 = 5.5 + 1.4x + -0.02x2 + -5.5 + -1.4x + 0.02x2 Combine like terms: x + -1.4x = -0.4x -5.5 + -0.4x + 0.02x2 = 5.5 + 1.4x + -0.02x2 + -5.5 + -1.4x + 0.02x2 Reorder the terms: -5.5 + -0.4x + 0.02x2 = 5.5 + -5.5 + 1.4x + -1.4x + -0.02x2 + 0.02x2 Combine like terms: 5.5 + -5.5 = 0.0 -5.5 + -0.4x + 0.02x2 = 0.0 + 1.4x + -1.4x + -0.02x2 + 0.02x2 -5.5 + -0.4x + 0.02x2 = 1.4x + -1.4x + -0.02x2 + 0.02x2 Combine like terms: 1.4x + -1.4x = 0.0 -5.5 + -0.4x + 0.02x2 = 0.0 + -0.02x2 + 0.02x2 -5.5 + -0.4x + 0.02x2 = -0.02x2 + 0.02x2 Combine like terms: -0.02x2 + 0.02x2 = 0.00 -5.5 + -0.4x + 0.02x2 = 0.00 Begin completing the square. Divide all terms by 0.02 the coefficient of the squared term: Divide each side by '0.02'. -275 + -20x + x2 = 0 Move the constant term to the right: Add '275' to each side of the equation. -275 + -20x + 275 + x2 = 0 + 275 Reorder the terms: -275 + 275 + -20x + x2 = 0 + 275 Combine like terms: -275 + 275 = 0 0 + -20x + x2 = 0 + 275 -20x + x2 = 0 + 275 Combine like terms: 0 + 275 = 275 -20x + x2 = 275 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = 275 + 100 Reorder the terms: 100 + -20x + x2 = 275 + 100 Combine like terms: 275 + 100 = 375 100 + -20x + x2 = 375 Factor a perfect square on the left side: (x + -10)(x + -10) = 375 Calculate the square root of the right side: 19.364916731 Break this problem into two subproblems by setting (x + -10) equal to 19.364916731 and -19.364916731.Subproblem 1
x + -10 = 19.364916731 Simplifying x + -10 = 19.364916731 Reorder the terms: -10 + x = 19.364916731 Solving -10 + x = 19.364916731 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 19.364916731 + 10 Combine like terms: -10 + 10 = 0 0 + x = 19.364916731 + 10 x = 19.364916731 + 10 Combine like terms: 19.364916731 + 10 = 29.364916731 x = 29.364916731 Simplifying x = 29.364916731Subproblem 2
x + -10 = -19.364916731 Simplifying x + -10 = -19.364916731 Reorder the terms: -10 + x = -19.364916731 Solving -10 + x = -19.364916731 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -19.364916731 + 10 Combine like terms: -10 + 10 = 0 0 + x = -19.364916731 + 10 x = -19.364916731 + 10 Combine like terms: -19.364916731 + 10 = -9.364916731 x = -9.364916731 Simplifying x = -9.364916731Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.364916731, -9.364916731}
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