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Simplifying -4.9x2 + 42x + -25 = 0 Reorder the terms: -25 + 42x + -4.9x2 = 0 Solving -25 + 42x + -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'. 5.102040816 + -8.571428571x + x2 = 0 Move the constant term to the right: Add '-5.102040816' to each side of the equation. 5.102040816 + -8.571428571x + -5.102040816 + x2 = 0 + -5.102040816 Reorder the terms: 5.102040816 + -5.102040816 + -8.571428571x + x2 = 0 + -5.102040816 Combine like terms: 5.102040816 + -5.102040816 = 0.000000000 0.000000000 + -8.571428571x + x2 = 0 + -5.102040816 -8.571428571x + x2 = 0 + -5.102040816 Combine like terms: 0 + -5.102040816 = -5.102040816 -8.571428571x + x2 = -5.102040816 The x term is -8.571428571x. Take half its coefficient (-4.285714286). Square it (18.36734694) and add it to both sides. Add '18.36734694' to each side of the equation. -8.571428571x + 18.36734694 + x2 = -5.102040816 + 18.36734694 Reorder the terms: 18.36734694 + -8.571428571x + x2 = -5.102040816 + 18.36734694 Combine like terms: -5.102040816 + 18.36734694 = 13.265306124 18.36734694 + -8.571428571x + x2 = 13.265306124 Factor a perfect square on the left side: (x + -4.285714286)(x + -4.285714286) = 13.265306124 Calculate the square root of the right side: 3.642156796 Break this problem into two subproblems by setting (x + -4.285714286) equal to 3.642156796 and -3.642156796.Subproblem 1
x + -4.285714286 = 3.642156796 Simplifying x + -4.285714286 = 3.642156796 Reorder the terms: -4.285714286 + x = 3.642156796 Solving -4.285714286 + x = 3.642156796 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.285714286' to each side of the equation. -4.285714286 + 4.285714286 + x = 3.642156796 + 4.285714286 Combine like terms: -4.285714286 + 4.285714286 = 0.000000000 0.000000000 + x = 3.642156796 + 4.285714286 x = 3.642156796 + 4.285714286 Combine like terms: 3.642156796 + 4.285714286 = 7.927871082 x = 7.927871082 Simplifying x = 7.927871082Subproblem 2
x + -4.285714286 = -3.642156796 Simplifying x + -4.285714286 = -3.642156796 Reorder the terms: -4.285714286 + x = -3.642156796 Solving -4.285714286 + x = -3.642156796 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.285714286' to each side of the equation. -4.285714286 + 4.285714286 + x = -3.642156796 + 4.285714286 Combine like terms: -4.285714286 + 4.285714286 = 0.000000000 0.000000000 + x = -3.642156796 + 4.285714286 x = -3.642156796 + 4.285714286 Combine like terms: -3.642156796 + 4.285714286 = 0.64355749 x = 0.64355749 Simplifying x = 0.64355749Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.927871082, 0.64355749}
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