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Simplifying -0.01x2 + 0.7x + 5.9 = 0 Reorder the terms: 5.9 + 0.7x + -0.01x2 = 0 Solving 5.9 + 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'. -590 + -70x + x2 = 0 Move the constant term to the right: Add '590' to each side of the equation. -590 + -70x + 590 + x2 = 0 + 590 Reorder the terms: -590 + 590 + -70x + x2 = 0 + 590 Combine like terms: -590 + 590 = 0 0 + -70x + x2 = 0 + 590 -70x + x2 = 0 + 590 Combine like terms: 0 + 590 = 590 -70x + x2 = 590 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 = 590 + 1225 Reorder the terms: 1225 + -70x + x2 = 590 + 1225 Combine like terms: 590 + 1225 = 1815 1225 + -70x + x2 = 1815 Factor a perfect square on the left side: (x + -35)(x + -35) = 1815 Calculate the square root of the right side: 42.602816808 Break this problem into two subproblems by setting (x + -35) equal to 42.602816808 and -42.602816808.Subproblem 1
x + -35 = 42.602816808 Simplifying x + -35 = 42.602816808 Reorder the terms: -35 + x = 42.602816808 Solving -35 + x = 42.602816808 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 = 42.602816808 + 35 Combine like terms: -35 + 35 = 0 0 + x = 42.602816808 + 35 x = 42.602816808 + 35 Combine like terms: 42.602816808 + 35 = 77.602816808 x = 77.602816808 Simplifying x = 77.602816808Subproblem 2
x + -35 = -42.602816808 Simplifying x + -35 = -42.602816808 Reorder the terms: -35 + x = -42.602816808 Solving -35 + x = -42.602816808 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 = -42.602816808 + 35 Combine like terms: -35 + 35 = 0 0 + x = -42.602816808 + 35 x = -42.602816808 + 35 Combine like terms: -42.602816808 + 35 = -7.602816808 x = -7.602816808 Simplifying x = -7.602816808Solution
The solution to the problem is based on the solutions from the subproblems. x = {77.602816808, -7.602816808}
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