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Simplifying -4.9x2 + 9x + 175 = 0 Reorder the terms: 175 + 9x + -4.9x2 = 0 Solving 175 + 9x + -4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -35.71428571 + -1.836734694x + x2 = 0 Move the constant term to the right: Add '35.71428571' to each side of the equation. -35.71428571 + -1.836734694x + 35.71428571 + x2 = 0 + 35.71428571 Reorder the terms: -35.71428571 + 35.71428571 + -1.836734694x + x2 = 0 + 35.71428571 Combine like terms: -35.71428571 + 35.71428571 = 0.00000000 0.00000000 + -1.836734694x + x2 = 0 + 35.71428571 -1.836734694x + x2 = 0 + 35.71428571 Combine like terms: 0 + 35.71428571 = 35.71428571 -1.836734694x + x2 = 35.71428571 The x term is -1.836734694x. Take half its coefficient (-0.918367347). Square it (0.8433985840) and add it to both sides. Add '0.8433985840' to each side of the equation. -1.836734694x + 0.8433985840 + x2 = 35.71428571 + 0.8433985840 Reorder the terms: 0.8433985840 + -1.836734694x + x2 = 35.71428571 + 0.8433985840 Combine like terms: 35.71428571 + 0.8433985840 = 36.557684294 0.8433985840 + -1.836734694x + x2 = 36.557684294 Factor a perfect square on the left side: (x + -0.918367347)(x + -0.918367347) = 36.557684294 Calculate the square root of the right side: 6.046295088 Break this problem into two subproblems by setting (x + -0.918367347) equal to 6.046295088 and -6.046295088.Subproblem 1
x + -0.918367347 = 6.046295088 Simplifying x + -0.918367347 = 6.046295088 Reorder the terms: -0.918367347 + x = 6.046295088 Solving -0.918367347 + x = 6.046295088 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.918367347' to each side of the equation. -0.918367347 + 0.918367347 + x = 6.046295088 + 0.918367347 Combine like terms: -0.918367347 + 0.918367347 = 0.000000000 0.000000000 + x = 6.046295088 + 0.918367347 x = 6.046295088 + 0.918367347 Combine like terms: 6.046295088 + 0.918367347 = 6.964662435 x = 6.964662435 Simplifying x = 6.964662435Subproblem 2
x + -0.918367347 = -6.046295088 Simplifying x + -0.918367347 = -6.046295088 Reorder the terms: -0.918367347 + x = -6.046295088 Solving -0.918367347 + x = -6.046295088 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.918367347' to each side of the equation. -0.918367347 + 0.918367347 + x = -6.046295088 + 0.918367347 Combine like terms: -0.918367347 + 0.918367347 = 0.000000000 0.000000000 + x = -6.046295088 + 0.918367347 x = -6.046295088 + 0.918367347 Combine like terms: -6.046295088 + 0.918367347 = -5.127927741 x = -5.127927741 Simplifying x = -5.127927741Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.964662435, -5.127927741}
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