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Simplifying 0 = -4.9x2 + 0.5x + 0.9 Reorder the terms: 0 = 0.9 + 0.5x + -4.9x2 Solving 0 = 0.9 + 0.5x + -4.9x2 Solving for variable 'x'. Combine like terms: 0 + -0.9 = -0.9 -0.9 + -0.5x + 4.9x2 = 0.9 + 0.5x + -4.9x2 + -0.9 + -0.5x + 4.9x2 Reorder the terms: -0.9 + -0.5x + 4.9x2 = 0.9 + -0.9 + 0.5x + -0.5x + -4.9x2 + 4.9x2 Combine like terms: 0.9 + -0.9 = 0.0 -0.9 + -0.5x + 4.9x2 = 0.0 + 0.5x + -0.5x + -4.9x2 + 4.9x2 -0.9 + -0.5x + 4.9x2 = 0.5x + -0.5x + -4.9x2 + 4.9x2 Combine like terms: 0.5x + -0.5x = 0.0 -0.9 + -0.5x + 4.9x2 = 0.0 + -4.9x2 + 4.9x2 -0.9 + -0.5x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -0.9 + -0.5x + 4.9x2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -0.1836734694 + -0.1020408163x + x2 = 0 Move the constant term to the right: Add '0.1836734694' to each side of the equation. -0.1836734694 + -0.1020408163x + 0.1836734694 + x2 = 0 + 0.1836734694 Reorder the terms: -0.1836734694 + 0.1836734694 + -0.1020408163x + x2 = 0 + 0.1836734694 Combine like terms: -0.1836734694 + 0.1836734694 = 0.0000000000 0.0000000000 + -0.1020408163x + x2 = 0 + 0.1836734694 -0.1020408163x + x2 = 0 + 0.1836734694 Combine like terms: 0 + 0.1836734694 = 0.1836734694 -0.1020408163x + x2 = 0.1836734694 The x term is -0.1020408163x. Take half its coefficient (-0.05102040815). Square it (0.002603082048) and add it to both sides. Add '0.002603082048' to each side of the equation. -0.1020408163x + 0.002603082048 + x2 = 0.1836734694 + 0.002603082048 Reorder the terms: 0.002603082048 + -0.1020408163x + x2 = 0.1836734694 + 0.002603082048 Combine like terms: 0.1836734694 + 0.002603082048 = 0.186276551448 0.002603082048 + -0.1020408163x + x2 = 0.186276551448 Factor a perfect square on the left side: (x + -0.05102040815)(x + -0.05102040815) = 0.186276551448 Calculate the square root of the right side: 0.431597673 Break this problem into two subproblems by setting (x + -0.05102040815) equal to 0.431597673 and -0.431597673.Subproblem 1
x + -0.05102040815 = 0.431597673 Simplifying x + -0.05102040815 = 0.431597673 Reorder the terms: -0.05102040815 + x = 0.431597673 Solving -0.05102040815 + x = 0.431597673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05102040815' to each side of the equation. -0.05102040815 + 0.05102040815 + x = 0.431597673 + 0.05102040815 Combine like terms: -0.05102040815 + 0.05102040815 = 0.00000000000 0.00000000000 + x = 0.431597673 + 0.05102040815 x = 0.431597673 + 0.05102040815 Combine like terms: 0.431597673 + 0.05102040815 = 0.48261808115 x = 0.48261808115 Simplifying x = 0.48261808115Subproblem 2
x + -0.05102040815 = -0.431597673 Simplifying x + -0.05102040815 = -0.431597673 Reorder the terms: -0.05102040815 + x = -0.431597673 Solving -0.05102040815 + x = -0.431597673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05102040815' to each side of the equation. -0.05102040815 + 0.05102040815 + x = -0.431597673 + 0.05102040815 Combine like terms: -0.05102040815 + 0.05102040815 = 0.00000000000 0.00000000000 + x = -0.431597673 + 0.05102040815 x = -0.431597673 + 0.05102040815 Combine like terms: -0.431597673 + 0.05102040815 = -0.38057726485 x = -0.38057726485 Simplifying x = -0.38057726485Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.48261808115, -0.38057726485}
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