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Simplifying 0 = -0.01x2 + -0.7x + 5.1 Reorder the terms: 0 = 5.1 + -0.7x + -0.01x2 Solving 0 = 5.1 + -0.7x + -0.01x2 Solving for variable 'x'. Combine like terms: 0 + -5.1 = -5.1 -5.1 + 0.7x + 0.01x2 = 5.1 + -0.7x + -0.01x2 + -5.1 + 0.7x + 0.01x2 Reorder the terms: -5.1 + 0.7x + 0.01x2 = 5.1 + -5.1 + -0.7x + 0.7x + -0.01x2 + 0.01x2 Combine like terms: 5.1 + -5.1 = 0.0 -5.1 + 0.7x + 0.01x2 = 0.0 + -0.7x + 0.7x + -0.01x2 + 0.01x2 -5.1 + 0.7x + 0.01x2 = -0.7x + 0.7x + -0.01x2 + 0.01x2 Combine like terms: -0.7x + 0.7x = 0.0 -5.1 + 0.7x + 0.01x2 = 0.0 + -0.01x2 + 0.01x2 -5.1 + 0.7x + 0.01x2 = -0.01x2 + 0.01x2 Combine like terms: -0.01x2 + 0.01x2 = 0.00 -5.1 + 0.7x + 0.01x2 = 0.00 Begin completing the square. Divide all terms by 0.01 the coefficient of the squared term: Divide each side by '0.01'. -510 + 70x + x2 = 0 Move the constant term to the right: Add '510' to each side of the equation. -510 + 70x + 510 + x2 = 0 + 510 Reorder the terms: -510 + 510 + 70x + x2 = 0 + 510 Combine like terms: -510 + 510 = 0 0 + 70x + x2 = 0 + 510 70x + x2 = 0 + 510 Combine like terms: 0 + 510 = 510 70x + x2 = 510 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 = 510 + 1225 Reorder the terms: 1225 + 70x + x2 = 510 + 1225 Combine like terms: 510 + 1225 = 1735 1225 + 70x + x2 = 1735 Factor a perfect square on the left side: (x + 35)(x + 35) = 1735 Calculate the square root of the right side: 41.653331199 Break this problem into two subproblems by setting (x + 35) equal to 41.653331199 and -41.653331199.Subproblem 1
x + 35 = 41.653331199 Simplifying x + 35 = 41.653331199 Reorder the terms: 35 + x = 41.653331199 Solving 35 + x = 41.653331199 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 = 41.653331199 + -35 Combine like terms: 35 + -35 = 0 0 + x = 41.653331199 + -35 x = 41.653331199 + -35 Combine like terms: 41.653331199 + -35 = 6.653331199 x = 6.653331199 Simplifying x = 6.653331199Subproblem 2
x + 35 = -41.653331199 Simplifying x + 35 = -41.653331199 Reorder the terms: 35 + x = -41.653331199 Solving 35 + x = -41.653331199 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 = -41.653331199 + -35 Combine like terms: 35 + -35 = 0 0 + x = -41.653331199 + -35 x = -41.653331199 + -35 Combine like terms: -41.653331199 + -35 = -76.653331199 x = -76.653331199 Simplifying x = -76.653331199Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.653331199, -76.653331199}
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