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Simplifying -0.01x2 + 0.7x + 6.7 = 0 Reorder the terms: 6.7 + 0.7x + -0.01x2 = 0 Solving 6.7 + 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'. -670 + -70x + x2 = 0 Move the constant term to the right: Add '670' to each side of the equation. -670 + -70x + 670 + x2 = 0 + 670 Reorder the terms: -670 + 670 + -70x + x2 = 0 + 670 Combine like terms: -670 + 670 = 0 0 + -70x + x2 = 0 + 670 -70x + x2 = 0 + 670 Combine like terms: 0 + 670 = 670 -70x + x2 = 670 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 = 670 + 1225 Reorder the terms: 1225 + -70x + x2 = 670 + 1225 Combine like terms: 670 + 1225 = 1895 1225 + -70x + x2 = 1895 Factor a perfect square on the left side: (x + -35)(x + -35) = 1895 Calculate the square root of the right side: 43.531597719 Break this problem into two subproblems by setting (x + -35) equal to 43.531597719 and -43.531597719.Subproblem 1
x + -35 = 43.531597719 Simplifying x + -35 = 43.531597719 Reorder the terms: -35 + x = 43.531597719 Solving -35 + x = 43.531597719 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 = 43.531597719 + 35 Combine like terms: -35 + 35 = 0 0 + x = 43.531597719 + 35 x = 43.531597719 + 35 Combine like terms: 43.531597719 + 35 = 78.531597719 x = 78.531597719 Simplifying x = 78.531597719Subproblem 2
x + -35 = -43.531597719 Simplifying x + -35 = -43.531597719 Reorder the terms: -35 + x = -43.531597719 Solving -35 + x = -43.531597719 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 = -43.531597719 + 35 Combine like terms: -35 + 35 = 0 0 + x = -43.531597719 + 35 x = -43.531597719 + 35 Combine like terms: -43.531597719 + 35 = -8.531597719 x = -8.531597719 Simplifying x = -8.531597719Solution
The solution to the problem is based on the solutions from the subproblems. x = {78.531597719, -8.531597719}
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