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Simplifying -3.5x2 + 0.3x + 0.7 = 0 Reorder the terms: 0.7 + 0.3x + -3.5x2 = 0 Solving 0.7 + 0.3x + -3.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -3.5 the coefficient of the squared term: Divide each side by '-3.5'. -0.2 + -0.08571428571x + x2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -0.08571428571x + 0.2 + x2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -0.08571428571x + x2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -0.08571428571x + x2 = 0 + 0.2 -0.08571428571x + x2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -0.08571428571x + x2 = 0.2 The x term is -0.08571428571x. Take half its coefficient (-0.04285714286). Square it (0.001836734694) and add it to both sides. Add '0.001836734694' to each side of the equation. -0.08571428571x + 0.001836734694 + x2 = 0.2 + 0.001836734694 Reorder the terms: 0.001836734694 + -0.08571428571x + x2 = 0.2 + 0.001836734694 Combine like terms: 0.2 + 0.001836734694 = 0.201836734694 0.001836734694 + -0.08571428571x + x2 = 0.201836734694 Factor a perfect square on the left side: (x + -0.04285714286)(x + -0.04285714286) = 0.201836734694 Calculate the square root of the right side: 0.449262434 Break this problem into two subproblems by setting (x + -0.04285714286) equal to 0.449262434 and -0.449262434.Subproblem 1
x + -0.04285714286 = 0.449262434 Simplifying x + -0.04285714286 = 0.449262434 Reorder the terms: -0.04285714286 + x = 0.449262434 Solving -0.04285714286 + x = 0.449262434 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04285714286' to each side of the equation. -0.04285714286 + 0.04285714286 + x = 0.449262434 + 0.04285714286 Combine like terms: -0.04285714286 + 0.04285714286 = 0.00000000000 0.00000000000 + x = 0.449262434 + 0.04285714286 x = 0.449262434 + 0.04285714286 Combine like terms: 0.449262434 + 0.04285714286 = 0.49211957686 x = 0.49211957686 Simplifying x = 0.49211957686Subproblem 2
x + -0.04285714286 = -0.449262434 Simplifying x + -0.04285714286 = -0.449262434 Reorder the terms: -0.04285714286 + x = -0.449262434 Solving -0.04285714286 + x = -0.449262434 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04285714286' to each side of the equation. -0.04285714286 + 0.04285714286 + x = -0.449262434 + 0.04285714286 Combine like terms: -0.04285714286 + 0.04285714286 = 0.00000000000 0.00000000000 + x = -0.449262434 + 0.04285714286 x = -0.449262434 + 0.04285714286 Combine like terms: -0.449262434 + 0.04285714286 = -0.40640529114 x = -0.40640529114 Simplifying x = -0.40640529114Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.49211957686, -0.40640529114}
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