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Simplifying -0.01x2 + 0.7x + 6.1 = 0 Reorder the terms: 6.1 + 0.7x + -0.01x2 = 0 Solving 6.1 + 0.7x + -0.01x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.01 the coefficient of the squared term: Divide each side by '-0.01'. -610 + -70x + x2 = 0 Move the constant term to the right: Add '610' to each side of the equation. -610 + -70x + 610 + x2 = 0 + 610 Reorder the terms: -610 + 610 + -70x + x2 = 0 + 610 Combine like terms: -610 + 610 = 0 0 + -70x + x2 = 0 + 610 -70x + x2 = 0 + 610 Combine like terms: 0 + 610 = 610 -70x + x2 = 610 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 = 610 + 1225 Reorder the terms: 1225 + -70x + x2 = 610 + 1225 Combine like terms: 610 + 1225 = 1835 1225 + -70x + x2 = 1835 Factor a perfect square on the left side: (x + -35)(x + -35) = 1835 Calculate the square root of the right side: 42.836899981 Break this problem into two subproblems by setting (x + -35) equal to 42.836899981 and -42.836899981.Subproblem 1
x + -35 = 42.836899981 Simplifying x + -35 = 42.836899981 Reorder the terms: -35 + x = 42.836899981 Solving -35 + x = 42.836899981 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 = 42.836899981 + 35 Combine like terms: -35 + 35 = 0 0 + x = 42.836899981 + 35 x = 42.836899981 + 35 Combine like terms: 42.836899981 + 35 = 77.836899981 x = 77.836899981 Simplifying x = 77.836899981Subproblem 2
x + -35 = -42.836899981 Simplifying x + -35 = -42.836899981 Reorder the terms: -35 + x = -42.836899981 Solving -35 + x = -42.836899981 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 = -42.836899981 + 35 Combine like terms: -35 + 35 = 0 0 + x = -42.836899981 + 35 x = -42.836899981 + 35 Combine like terms: -42.836899981 + 35 = -7.836899981 x = -7.836899981 Simplifying x = -7.836899981Solution
The solution to the problem is based on the solutions from the subproblems. x = {77.836899981, -7.836899981}
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