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Simplifying -0.005x2 + 0.7x + 3.5 = 0 Reorder the terms: 3.5 + 0.7x + -0.005x2 = 0 Solving 3.5 + 0.7x + -0.005x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.005 the coefficient of the squared term: Divide each side by '-0.005'. -700 + -140x + x2 = 0 Move the constant term to the right: Add '700' to each side of the equation. -700 + -140x + 700 + x2 = 0 + 700 Reorder the terms: -700 + 700 + -140x + x2 = 0 + 700 Combine like terms: -700 + 700 = 0 0 + -140x + x2 = 0 + 700 -140x + x2 = 0 + 700 Combine like terms: 0 + 700 = 700 -140x + x2 = 700 The x term is -140x. Take half its coefficient (-70). Square it (4900) and add it to both sides. Add '4900' to each side of the equation. -140x + 4900 + x2 = 700 + 4900 Reorder the terms: 4900 + -140x + x2 = 700 + 4900 Combine like terms: 700 + 4900 = 5600 4900 + -140x + x2 = 5600 Factor a perfect square on the left side: (x + -70)(x + -70) = 5600 Calculate the square root of the right side: 74.833147735 Break this problem into two subproblems by setting (x + -70) equal to 74.833147735 and -74.833147735.Subproblem 1
x + -70 = 74.833147735 Simplifying x + -70 = 74.833147735 Reorder the terms: -70 + x = 74.833147735 Solving -70 + x = 74.833147735 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '70' to each side of the equation. -70 + 70 + x = 74.833147735 + 70 Combine like terms: -70 + 70 = 0 0 + x = 74.833147735 + 70 x = 74.833147735 + 70 Combine like terms: 74.833147735 + 70 = 144.833147735 x = 144.833147735 Simplifying x = 144.833147735Subproblem 2
x + -70 = -74.833147735 Simplifying x + -70 = -74.833147735 Reorder the terms: -70 + x = -74.833147735 Solving -70 + x = -74.833147735 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '70' to each side of the equation. -70 + 70 + x = -74.833147735 + 70 Combine like terms: -70 + 70 = 0 0 + x = -74.833147735 + 70 x = -74.833147735 + 70 Combine like terms: -74.833147735 + 70 = -4.833147735 x = -4.833147735 Simplifying x = -4.833147735Solution
The solution to the problem is based on the solutions from the subproblems. x = {144.833147735, -4.833147735}
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