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Simplifying 300 = 4.9x2 + 3x Reorder the terms: 300 = 3x + 4.9x2 Solving 300 = 3x + 4.9x2 Solving for variable 'x'. Reorder the terms: 300 + -3x + -4.9x2 = 3x + -3x + 4.9x2 + -4.9x2 Combine like terms: 3x + -3x = 0 300 + -3x + -4.9x2 = 0 + 4.9x2 + -4.9x2 300 + -3x + -4.9x2 = 4.9x2 + -4.9x2 Combine like terms: 4.9x2 + -4.9x2 = 0.0 300 + -3x + -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'. -61.2244898 + 0.612244898x + x2 = 0 Move the constant term to the right: Add '61.2244898' to each side of the equation. -61.2244898 + 0.612244898x + 61.2244898 + x2 = 0 + 61.2244898 Reorder the terms: -61.2244898 + 61.2244898 + 0.612244898x + x2 = 0 + 61.2244898 Combine like terms: -61.2244898 + 61.2244898 = 0.0000000 0.0000000 + 0.612244898x + x2 = 0 + 61.2244898 0.612244898x + x2 = 0 + 61.2244898 Combine like terms: 0 + 61.2244898 = 61.2244898 0.612244898x + x2 = 61.2244898 The x term is 0.612244898x. Take half its coefficient (0.306122449). Square it (0.09371095378) and add it to both sides. Add '0.09371095378' to each side of the equation. 0.612244898x + 0.09371095378 + x2 = 61.2244898 + 0.09371095378 Reorder the terms: 0.09371095378 + 0.612244898x + x2 = 61.2244898 + 0.09371095378 Combine like terms: 61.2244898 + 0.09371095378 = 61.31820075378 0.09371095378 + 0.612244898x + x2 = 61.31820075378 Factor a perfect square on the left side: (x + 0.306122449)(x + 0.306122449) = 61.31820075378 Calculate the square root of the right side: 7.830593895 Break this problem into two subproblems by setting (x + 0.306122449) equal to 7.830593895 and -7.830593895.Subproblem 1
x + 0.306122449 = 7.830593895 Simplifying x + 0.306122449 = 7.830593895 Reorder the terms: 0.306122449 + x = 7.830593895 Solving 0.306122449 + x = 7.830593895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.306122449' to each side of the equation. 0.306122449 + -0.306122449 + x = 7.830593895 + -0.306122449 Combine like terms: 0.306122449 + -0.306122449 = 0.000000000 0.000000000 + x = 7.830593895 + -0.306122449 x = 7.830593895 + -0.306122449 Combine like terms: 7.830593895 + -0.306122449 = 7.524471446 x = 7.524471446 Simplifying x = 7.524471446Subproblem 2
x + 0.306122449 = -7.830593895 Simplifying x + 0.306122449 = -7.830593895 Reorder the terms: 0.306122449 + x = -7.830593895 Solving 0.306122449 + x = -7.830593895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.306122449' to each side of the equation. 0.306122449 + -0.306122449 + x = -7.830593895 + -0.306122449 Combine like terms: 0.306122449 + -0.306122449 = 0.000000000 0.000000000 + x = -7.830593895 + -0.306122449 x = -7.830593895 + -0.306122449 Combine like terms: -7.830593895 + -0.306122449 = -8.136716344 x = -8.136716344 Simplifying x = -8.136716344Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.524471446, -8.136716344}
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