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Simplifying 9 = 0.08x2 + 1.6x + 2 Reorder the terms: 9 = 2 + 1.6x + 0.08x2 Solving 9 = 2 + 1.6x + 0.08x2 Solving for variable 'x'. Combine like terms: 9 + -2 = 7 7 + -1.6x + -0.08x2 = 2 + 1.6x + 0.08x2 + -2 + -1.6x + -0.08x2 Reorder the terms: 7 + -1.6x + -0.08x2 = 2 + -2 + 1.6x + -1.6x + 0.08x2 + -0.08x2 Combine like terms: 2 + -2 = 0 7 + -1.6x + -0.08x2 = 0 + 1.6x + -1.6x + 0.08x2 + -0.08x2 7 + -1.6x + -0.08x2 = 1.6x + -1.6x + 0.08x2 + -0.08x2 Combine like terms: 1.6x + -1.6x = 0.0 7 + -1.6x + -0.08x2 = 0.0 + 0.08x2 + -0.08x2 7 + -1.6x + -0.08x2 = 0.08x2 + -0.08x2 Combine like terms: 0.08x2 + -0.08x2 = 0.00 7 + -1.6x + -0.08x2 = 0.00 Begin completing the square. Divide all terms by -0.08 the coefficient of the squared term: Divide each side by '-0.08'. -87.5 + 20x + x2 = 0 Move the constant term to the right: Add '87.5' to each side of the equation. -87.5 + 20x + 87.5 + x2 = 0 + 87.5 Reorder the terms: -87.5 + 87.5 + 20x + x2 = 0 + 87.5 Combine like terms: -87.5 + 87.5 = 0.0 0.0 + 20x + x2 = 0 + 87.5 20x + x2 = 0 + 87.5 Combine like terms: 0 + 87.5 = 87.5 20x + x2 = 87.5 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 = 87.5 + 100 Reorder the terms: 100 + 20x + x2 = 87.5 + 100 Combine like terms: 87.5 + 100 = 187.5 100 + 20x + x2 = 187.5 Factor a perfect square on the left side: (x + 10)(x + 10) = 187.5 Calculate the square root of the right side: 13.693063938 Break this problem into two subproblems by setting (x + 10) equal to 13.693063938 and -13.693063938.Subproblem 1
x + 10 = 13.693063938 Simplifying x + 10 = 13.693063938 Reorder the terms: 10 + x = 13.693063938 Solving 10 + x = 13.693063938 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 = 13.693063938 + -10 Combine like terms: 10 + -10 = 0 0 + x = 13.693063938 + -10 x = 13.693063938 + -10 Combine like terms: 13.693063938 + -10 = 3.693063938 x = 3.693063938 Simplifying x = 3.693063938Subproblem 2
x + 10 = -13.693063938 Simplifying x + 10 = -13.693063938 Reorder the terms: 10 + x = -13.693063938 Solving 10 + x = -13.693063938 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 = -13.693063938 + -10 Combine like terms: 10 + -10 = 0 0 + x = -13.693063938 + -10 x = -13.693063938 + -10 Combine like terms: -13.693063938 + -10 = -23.693063938 x = -23.693063938 Simplifying x = -23.693063938Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.693063938, -23.693063938}
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