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Simplifying x = 0.1x2 + 8x + -50 Reorder the terms: x = -50 + 8x + 0.1x2 Solving x = -50 + 8x + 0.1x2 Solving for variable 'x'. Reorder the terms: 50 + x + -8x + -0.1x2 = -50 + 8x + 0.1x2 + 50 + -8x + -0.1x2 Combine like terms: x + -8x = -7x 50 + -7x + -0.1x2 = -50 + 8x + 0.1x2 + 50 + -8x + -0.1x2 Reorder the terms: 50 + -7x + -0.1x2 = -50 + 50 + 8x + -8x + 0.1x2 + -0.1x2 Combine like terms: -50 + 50 = 0 50 + -7x + -0.1x2 = 0 + 8x + -8x + 0.1x2 + -0.1x2 50 + -7x + -0.1x2 = 8x + -8x + 0.1x2 + -0.1x2 Combine like terms: 8x + -8x = 0 50 + -7x + -0.1x2 = 0 + 0.1x2 + -0.1x2 50 + -7x + -0.1x2 = 0.1x2 + -0.1x2 Combine like terms: 0.1x2 + -0.1x2 = 0.0 50 + -7x + -0.1x2 = 0.0 Begin completing the square. Divide all terms by -0.1 the coefficient of the squared term: Divide each side by '-0.1'. -500 + 70x + x2 = 0 Move the constant term to the right: Add '500' to each side of the equation. -500 + 70x + 500 + x2 = 0 + 500 Reorder the terms: -500 + 500 + 70x + x2 = 0 + 500 Combine like terms: -500 + 500 = 0 0 + 70x + x2 = 0 + 500 70x + x2 = 0 + 500 Combine like terms: 0 + 500 = 500 70x + x2 = 500 The x term is 70x. Take half its coefficient (35). Square it (1225) and add it to both sides. Add '1225' to each side of the equation. 70x + 1225 + x2 = 500 + 1225 Reorder the terms: 1225 + 70x + x2 = 500 + 1225 Combine like terms: 500 + 1225 = 1725 1225 + 70x + x2 = 1725 Factor a perfect square on the left side: (x + 35)(x + 35) = 1725 Calculate the square root of the right side: 41.533119315 Break this problem into two subproblems by setting (x + 35) equal to 41.533119315 and -41.533119315.Subproblem 1
x + 35 = 41.533119315 Simplifying x + 35 = 41.533119315 Reorder the terms: 35 + x = 41.533119315 Solving 35 + x = 41.533119315 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-35' to each side of the equation. 35 + -35 + x = 41.533119315 + -35 Combine like terms: 35 + -35 = 0 0 + x = 41.533119315 + -35 x = 41.533119315 + -35 Combine like terms: 41.533119315 + -35 = 6.533119315 x = 6.533119315 Simplifying x = 6.533119315Subproblem 2
x + 35 = -41.533119315 Simplifying x + 35 = -41.533119315 Reorder the terms: 35 + x = -41.533119315 Solving 35 + x = -41.533119315 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-35' to each side of the equation. 35 + -35 + x = -41.533119315 + -35 Combine like terms: 35 + -35 = 0 0 + x = -41.533119315 + -35 x = -41.533119315 + -35 Combine like terms: -41.533119315 + -35 = -76.533119315 x = -76.533119315 Simplifying x = -76.533119315Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.533119315, -76.533119315}
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